# Application 22-27 Flashcards

## solve problem questions

Shares of closed-end fund ABC were selling at

a premium of 10% and then fell to $44 per share while ABC’s net asset value

held constant at $50 per share. What were the previous market price,

subsequent discount, NAV-based return, and market-price return for ABC?

previous market price:

1 + premium x net asset value

1 + 0.10 x 50

= 55

subsequent discount:

fall in price / net asset value (- 1)

44 / 55 (- 1)

= -0.12 (-12%)

market price return:

fall in price - net asset value / net asset value

44 - 55 / 55 = -0.20 (20%)

Shares of closed-end fund ABC were selling at

a premium of 12% and then fell to $40 per share while ABC’s net asset value

held constant at $40 per share. What were the previous market price,

subsequent discount, NAV-based return, and market-price return for ABC?

previous market price return:

1 + 0.12 x 40

= 44.8

NAV-based return:

40 / 40 (-1) = 0

Subsequent discount:

40 - 44.80 / 44.80

= -0.1071 (-10.71%)

Shares of closed-end fund ABC were selling at

a premium of 12% and then fell to $20 per share while ABC’s net asset value

held constant at $20 per share. What were the previous market price,

subsequent discount, NAV-based return, and market-price return for ABC?

?

Shares of closed-end fund ABC were selling at

a premium of 5% and then fell to $16 per share while ABC’s net asset value

held constant at $20 per share. What were the previous market price,

subsequent discount, NAV-based return, and market-price return for ABC?

?

Shares of closed-end fund ABC were selling at

a premium of 1% and then fell to $30 per share while ABC’s net asset value

held constant at $30 per share. What were the previous market price,

subsequent discount, NAV-based return, and market-price return for ABC?

?

Shares of closed-end fund ABC were selling at

a premium of 3% and then fell to $18 per share while ABC’s net asset value

held constant at $20 per share. What were the previous market price,

subsequent discount, NAV-based return, and market-price return for ABC?

?

Shares of closed-end fund ABC were selling at

a premium of 2% and then fell to $22 per share while ABC’s net asset value

held constant at $25 per share. What were the previous market price,

subsequent discount, NAV-based return, and market-price return for ABC?

?

A convertible preferred stock with a par or face

value of $100 per share is convertible into four shares of common stock. What is

the conversion ratio, and what is the conversion price? What would be the

conversion ratio if the conversion price were $20?

conversion price:

four shares of common stock with value of $100

100 / 4 = $25

conversion ratio of $20:

100/20 = 5/1

A convertible preferred stock with a par or face

value of $100 per share is convertible into four shares of common stock. What would be the

conversion ratio if the conversion price were $50?

?

A convertible preferred stock with a par or face

value of $350 per share is convertible into four shares of common stock. What is

the conversion ratio, and what is the conversion price? What would be the

conversion ratio if the conversion price were $50?

?

A convertible preferred stock with a par or face

value of $250 per share is convertible into four shares of common stock. What is

the conversion ratio, and what is the conversion price? What would be the

conversion ratio if the conversion price were $83.33?

?

A convertible preferred stock with a par or face

value of $450 per share is convertible into four shares of common stock. What is

the conversion ratio, and what is the conversion price? What would be the

conversion ratio if the conversion price were $90?

?

A convertible preferred stock with a par or face

value of $750 per share is convertible into four shares of common stock. What is

the conversion ratio, and what is the conversion price? What would be the

conversion ratio if the conversion price were $187.50?

?

A VC fund manager raises $100 million in

committed capital for his VC fund. The management fee is 2.5%. To date, only

$50 million of the raised capital has been called and invested in start-ups. What

would be the annual management fee?

annual management fee:

capital committed capital for VC x management fee %

100,000,000 x 0.025

= 2,500,000 (even though not all capital has been invested)

A VC fund manager raises $100 million in

committed capital for his VC fund. The management fee is 1%. To date, only

$70 million of the raised capital has been called and invested in start-ups. What

would be the annual management fee?

?

A VC fund manager raises $500 million in

committed capital for his VC fund. The management fee is 2%. To date, only

$400 million of the raised capital has been called and invested in start-ups. What

would be the annual management fee?

?

Suppose

that all other facts remain the same, initial investment $100 million valuation cash flow $120 million, growth rate 2%, except that the discount rate used at the end

of seven years is 15%.

the new rate of return is:

valuation cash flow / (discount rate - growth rate)

120,000,000 / (0.15 - 0.02)

= $923 million

923,000,000,000/ 100,000,000,000 ^(1/7) (-1)

= 0.374 (37.4%)

1/7 because it is over seven years.

Suppose

that all other facts remain the same, initial investment $100 million valuation cash flow $120 million, growth rate 5%, except that the discount rate used at the end

of seven years is 12%.

(1,714,285,714,284,714/100,000,000,000)^1/7 (-1)

new valuation:

120,000,000,000 / (0.12-0.05)

= 1,714,285,714,284,714

Suppose

that all other facts remain the same, initial investment $100 million valuation cash flow $120 million, growth rate 2%, except that the discount rate used at the end

of seven years is 12%.

?

Suppose

that all other facts remain the same, initial investment $100 million valuation cash flow $120 million, growth rate 7%, except that the discount rate used at the end

of seven years is 12%.

?

Suppose

that all other facts remain the same, initial investment $100 million valuation cash flow $120 million, growth rate 1%, except that the discount rate used at the end

of seven years is 14%.

?

Suppose

that all other facts remain the same, initial investment $100 million valuation cash flow $120 million, growth rate 2%, except that the discount rate used at the end

of eight years is 15%.

?

Suppose

that all other facts remain the same, initial investment $100 million valuation cash flow $120 million, growth rate 5%, except that the discount rate used at the end

of eight years is 12%.

?

Suppose

that all other facts remain the same, initial investment $100 million valuation cash flow $120 million, growth rate 2%, except that the discount rate used at the end

of eight years is 12%.

?

Suppose

that all other facts remain the same, initial investment $100 million except that the $120 million cash flow estimate

given is a year 7 cash flow that is anticipated to grow by year 8.

120 (1.02) / 0.12 - 0.02)

= $1.224 billion

$1,224 billion / $100 million ^1/7 (- 1)

= 43%

Suppose that the structure on the right-hand side

of Exhibit 24.1 is changed such that the mezzanine debt rises to being 30% of

the capital structure, and the bank debt falls to being 50% of the capital structure.

If the costs of bank debt and equity remain the same (8% and 32%, respectively),

what must the new cost of mezzanine debt be such that the weighted average

cost of capital would be 15.8%?

Cost of equity 20.00%.

WACC = C(a) x P(a) + C(b) x P(b) + C(c) x P(c)

0.158 = C(a) x 0.30 + 0.32 x (-0.20) + (-0.08) x 0.50

manipulate equation

= 0.18

Suppose that the structure on the right-hand side

of Exhibit 24.1 is changed such that the mezzanine debt rises to being 25% of

the capital structure, and the bank debt falls to being 50% of the capital structure.

If the costs of bank debt and equity remain the same (8% and 30%, respectively),

what must the new cost of mezzanine debt be such that the weighted average

cost of capital would be 13.25%?

Cost of equity 22.00%.

?

Suppose that the structure on the right-hand side

of Exhibit 24.1 is changed such that the mezzanine debt rises to being 25% of

the capital structure, and the bank debt falls to being 50% of the capital structure.

If the costs of bank debt and equity remain the same (8% and 25%, respectively),

what must the new cost of mezzanine debt be such that the weighted average

cost of capital would be 12.5%?

Cost of equity 22.00%.

?

Suppose that the structure on the right-hand side

of Exhibit 24.1 is changed such that the mezzanine debt rises to being 15% of

the capital structure, and the bank debt falls to being 55% of the capital structure.

If the costs of bank debt and equity remain the same (8% and 30%, respectively),

what must the new cost of mezzanine debt be such that the weighted average

cost of capital would be 13.25%?

Cost of equity 23.00%.

?

Suppose that the structure on the right-hand side

of Exhibit 24.1 is changed such that the mezzanine debt rises to being 20% of

the capital structure, and the bank debt falls to being 55% of the capital structure.

If the costs of bank debt and equity remain the same (8% and 25%, respectively),

what must the new cost of mezzanine debt be such that the weighted average

cost of capital would be 13%?

Cost of equity 24.00%.

?

Suppose that the structure on the right-hand side

of Exhibit 24.1 is changed such that the mezzanine debt rises to being 15% of

the capital structure, and the bank debt falls to being 60% of the capital structure.

If the costs of bank debt and equity remain the same (8% and 25%, respectively),

what must the new cost of mezzanine debt be such that the weighted average

cost of capital would be 13.15%?

Cost of equity 25.00%.

?

Suppose that the structure on the right-hand side

of Exhibit 24.1 is changed such that the mezzanine debt rises to being 14% of

the capital structure, and the bank debt falls to being 60% of the capital structure.

If the costs of bank debt and equity remain the same (8% and 20%, respectively),

what must the new cost of mezzanine debt be such that the weighted average

cost of capital would be 13.20%?

Cost of equity 28.00%.

?

If 20% of the bonds in a portfolio default each

year and if 60% of the bonds’ value is ultimately unrecovered (i.e., 40% of the

bonds’ cost is recovered), then the total loss due to default over that time period

is?

(Coupon rate) Total Loss Due to Default:

Annual Default x Loss Rate Given Default

0.20% x 0.40%

= 0.12%

If 30% of the bonds in a portfolio default each

year and if 80% of the bonds’ value is ultimately unrecovered (i.e., 40% of the

bonds’ cost is recovered), then the total loss due to default over that time period

is?

coupon rate = bond default x bond value

0.30% x 0.80% = 0.24%

If 20% of the bonds in a portfolio default each

year and if 30% of the bonds’ value is ultimately unrecovered (i.e., 40% of the

bonds’ cost is recovered), then the total loss due to default over that time period

is?

?

If 15% of the bonds in a portfolio default each

year and if 5% of the bonds’ value is ultimately unrecovered (i.e., 40% of the

bonds’ cost is recovered), then the total loss due to default over that time period

is?

?

If 25% of the bonds in a portfolio default each

year and if 80% of the bonds’ value is ultimately unrecovered (i.e., 40% of the

bonds’ cost is recovered), then the total loss due to default over that time period

is?

?

If 30% of the bonds in a portfolio default each

year and if 70% of the bonds’ value is ultimately unrecovered (i.e., 40% of the

bonds’ cost is recovered), then the total loss due to default over that time period

is?

?

If 40% of the bonds in a portfolio default each

year and if 65% of the bonds’ value is ultimately unrecovered (i.e., 40% of the

bonds’ cost is recovered), then the total loss due to default over that time period

is?

?

Consider a firm with $50 million in assets and

$25 million in equity value. The firm has one debt issue: a zero-coupon bond

maturing in one year with a face value of $30 million. A riskless zero-coupon

bond of the same maturity sells for 90% of its face value. What is the value of the

firm’s debt? What is the value of a one-year put option on the firm’s assets with a

strike price of $30 million?

Assets = (Call) + (Riskless Bond - Put)

Assets - Call = Debt = Riskless Bond - Put

50,000,000 - 25,000,000 = (30,000,000 x 0.9) - Put

25,000,000 = 27,000,000 - Put

Put = 2,000,000

Consider a firm with $25 million in assets and

$5 million in equity value. The firm has one debt issue: a zero-coupon bond

maturing in one year with a face value of $25 million. A riskless zero-coupon

bond of the same maturity sells for 85% of its face value. What is the value of the

firm’s debt? What is the value of a one-year put option on the firm’s assets with a

strike price of $25 million?

asset - call = face value (face value %) - Put

25 - 5 = 25 (0.85) - Put

20 = 21.2500,000 - Put

Put = 1,250,000

Consider a firm with $25 million in assets and

$10 million in equity value. The firm has one debt issue: a zero-coupon bond

maturing in one year with a face value of $20 million. A riskless zero-coupon

bond of the same maturity sells for 95% of its face value. What is the value of the

firm’s debt? What is the value of a one-year put option on the firm’s assets with a

strike price of $20 million?

?

Consider a firm with $50 million in assets and

$25 million in equity value. The firm has one debt issue: a zero-coupon bond

maturing in one year with a face value of $35 million. A riskless zero-coupon

bond of the same maturity sells for 80% of its face value. What is the value of the

firm’s debt? What is the value of a one-year put option on the firm’s assets with a

strike price of $35 million?

?

Consider a firm with $75 million in assets and

$30 million in equity value. The firm has one debt issue: a zero-coupon bond

maturing in one year with a face value of $48 million. A riskless zero-coupon

bond of the same maturity sells for 90% of its face value. What is the value of the

firm’s debt? What is the value of a one-year put option on the firm’s assets with a

strike price of $48 million?

?

Consider a firm with $55 million in assets and

$50 million in equity value. The firm has one debt issue: a zero-coupon bond

maturing in one year with a face value of $7 million. A riskless zero-coupon

bond of the same maturity sells for 75% of its face value. What is the value of the

firm’s debt? What is the value of a one-year put option on the firm’s assets with a

strike price of $7 million?

?

Consider a firm with $65 million in assets and

$55 million in equity value. The firm has one debt issue: a zero-coupon bond

maturing in one year with a face value of $20 million. A riskless zero-coupon

bond of the same maturity sells for 65% of its face value. What is the value of the

firm’s debt? What is the value of a one-year put option on the firm’s assets with a

strike price of $20 million?

?