Question

Consider the following two mutually exclusive alternatives for reclaiming a deteriorating inner-city neighborhood (one of them must be chosen). Notice that the IRR for both alternatives is 27.19%.

Alternatives
EOY X Y
0 -$100,000 -$100,000
1 $50,000 0
2 $51,000 0
3 $60,000 $205,760
1RR 27.19% 27.19%
a. which alternative should be chosen if MARR is 15% per year
b. If MARR is 15% per year, which alternative is better?
c. What is the IRR on the incremental cash flow [i.e., ∆(Y − X)]?
d. If the MARR is 27.5% per year, which alternative is better?
e. What is the simple payback period for each alternative?
f. Which alternative would you recommend?

Answer 1

a) alternative Y should be chosen

b) alternative Y, because its NPV is higher

c) 27.19%

d) alternative X, because its NPV is only -$463 (alternative Y's NPV = - $727)

e) alternative X = 1.98 years

alternative Y = 2.49 years

f) alternative Y because its NPV is much higher when MARR = 15%, and when MARR increased to 27.5%, the difference between both projects' NPV was very small.

Step-by-step explanation:

a and b)

NPV of alternative X = -$100,000 + $50,000/1.15 + $51,000/1.15² + $60,000/1.15³ = -$100,000 + $43,478 + $38,563 + $39,451 = $21,492

NPV of alternative Y = -$100,000 + $205,760/1.15³ = $35,291

c)

incremental cash flows:

-$50,000

-$51,000

$145,760

TIR = 27.19%

d)

NPV of alternative X = -$100,000 + $50,000/1.275 + $51,000/1.275² + $60,000/1.275³ = -$100,000 + $39,216 + $31,373 + $28,948 = -$463

NPV of alternative Y = -$100,000 + $205,760/1.275³ = -$727

e)

alternative X ⇒ 1 year + ($50,000 / $51,000) = 1.98 years

alternative Y ⇒ 2 years + ($100,000 / $205,760) = 2.49 years