5. Investment Decision Making

Question 1

Discounting Formula - Present Value

Answer 1

Receiving a sum of money in the future is worth less than if we received it today so we must discount it to find the present value.

(1+r)^-n

$ * (1+r)^-n = PV.

Question 2

Compounding formula - Terminal Value

Answer 2

Investing a sum of money will earn interest and increase the value so to find out the future value of a sum we must compound it to find the Terminal Value.

(1+r)^n

$ * (1+r)^n = TV.

Question 3

NPV vs IRR vs MIRR

Modified IRR

Answer 3

NPV considers the time value of money and uses discounted cash flow (DCF) techniques. NPV is the net benefit or loss of benefit in present value terms from an investment opportunity. NPV represents surplus funds earned on the project and therefore is an indication on the impact the investment would have on shareholder wealth

NPV is weighted more than IRR when appraising investment opportunities.

IRR is the rate of return at at which the project has an NPV of zero.

IRR > WACC = Project should be accepted with caveat that NPV should be positive.

MIRR (Modified IRR)
Investment phase (cash outflow stage) - PV I
Return phase (cash inflow stages) - PV R
Cost of capital % - re

(PV R / PV I) ^1/n (1+re) -1

MIRR gives an indication of the maximum level of investment the firm could sustain that would allow the project to remain worthwhile.`

Question 4

Annuities, Delayed Annuities and Perpetuities

Answer 4

Annuity is a constant sum of money that will be received for a set number of years.

• Use annutiy table (PV table)

Delayed annuity
- Use annuity table for years of cash inflow. This will then give you the annuity of the cash inflows at the Tn-1 (Tn being the period cash inflows begin)
- Then discount this from Tn-1 back to T0.
example:
Cash inflow received for 4 years starting in 3 years time.
1. Discount the annuity over 4 years, this will give you the annuity value at T2 (which equals T3-1)
2. Discount the answer at Step 1 (T2) back to T0 (2 years) at discount rate provided.
3. This would give you the PV of a delayed annuity.

Perpetuity is a constant sum of money that will be received for the foreseeable future (indefinetely)

• PV = Cashflow / r

Be careful that any monies received immediately are not discounted and so the annuity rate would apply to the remaining years ( total years -1), and the initial sum added in full.

Question 5

Profitability Index and Discounted Payback Profitability Index

Answer 5

Profitability Index (PI):
= NPV of project / Cash outflow (Initial Investment)

PI is used to rank projects in order to allocate funds.

Discounted Payback Profitability Index (DPPI):
= PV of net cash inflows / Initial cash outlay (initial investment)

This is a measure of the number of times a project recovers the initial funds invested, which is particularly important if funds are scarce.