Question

Calculate the profitability indexes of the two pairs of mutually exclusive
investments in Self-Tests 8.3 and 8.4. Use a 7.5% discount rate. Does the
profitability index give the right ranking in each case?

8.4 self test:

Your wacky benefactor (see Self-Test 8.3) now offers you the choice of two
opportunities:
a. Invest $1,000 today and quadruple your money—a 300% return—in 1 year
with no risk.
b. Invest $1 million for 1 year at a guaranteed 50% return.
Which will you take? Do you want to earn a wonderful rate of return (300%),
or do you want to be rich? Safe securities still yield 7.5%.

8.3 self test:

A rich, friendly, and probably slightly unbalanced benefactor offers you the
opportunity to invest $1 million in two mutually exclusive ways. The payoffs are:
a. $2 million after 1 year, a 100% return
b. $300,000 a year forever
Neither investment is risky, and safe securities are yielding 7.5%. Which
investment will you take? You can’t take both, so the choices are mutually
exclusive. Do you want to earn a high percentage return, or do you want to be
rich? By the way, if you really had this investment opportunity, you’d have no
trouble borrowing the money to undertake it.

Answer 1

Profitability index = (PV of future cash flows) / Initial investment

Self test 8.3 :

a) Initial investment = $ 1 million

Future value after 1 year (FV) = $ 2 million , n = 1 year , given discount rate = 7.5 %

PV of future cash flow = FV / ( (1+r)^n) = $ 2000000 / ((1+7.5%)^1) = $ 1860465

Profitability Index (PI) = (PV of future cash flows) / Initial investment = $ 1860465/ $ 1000000 = 1.86

b) Perpetual cash flow = $ 300000

PV of perpetual cash flow = Perpetuity / discount rate = $300000/ 7.5% = $4000000

Profitability Index (PI) = (PV of future cash flows) / Initial investment = $ 4000000/ $ 1000000 = 4

Here option b) should be chosen as profitability Index is higher for option b) than a) .

Self test 8.4

a) Initial investment = $ 1000

Future value after 1 year (FV) = $4000 (300% return = 1000+3000 = 4000) , n = 1 year , given discount rate = 7.5 %

PV of future cash flow = FV / ( (1+r)^n) = $ 4000 / ((1+7.5%)^1) = $ 3720.90

Profitability Index (PI) = (PV of future cash flows) / Initial investment = $ 3720.90/ $ 1000 = 3.72

b) Initial investment = $ 1 million

Future value after 1 year (FV) = $1.5 million (1000000+50%* 1000000) , n = 1 year , given discount rate = 7.5 %

PV of future cash flow = FV / ( (1+r)^n) = $ 1500000 / ((1+7.5%)^1) = $ 1395349

Profitability Index (PI) = (PV of future cash flows) / Initial investment = $ 1395349/ $ 1000000 = 1.395

In this case option a) would be preferred as it gives higher PI than option b)