Question

Seether, Inc., has the following two mutually exclusive projects available.

Year	Project R		Project S
0	–$	55,000	–$	76,000
1		21,000		20,000
2		22,000		20,000
3		19,000		35,000
4		12,000		30,000
5		9,000		10,000
Requirement 1: What is the crossover rate for these two projects? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)   Internal rate of return % Requirement 2: What is the NPV of each project at the crossover rate? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)     NPV   Project R $      Project S $

Answer 1

Answer

Requirement -1 : Crossover Rate of two projects is the rate of return where the NPV of two projects becomes equal.

NPV_R = NPV_S

-55000 + 21000/ (1+r) +22000/ (1+r)² + 19000/ (1+r)³ + 12000/ (1+r)⁴ + 9000/ (1+r)⁵ = -76000 + 20000/ (1+r) +20000/ (1+r)² + 35000/ (1+r)³ + 30000/ (1+r)⁴ + 10000/ (1+r)⁵

21000 + 1000/ (1+r) +2000/ (1+r)² - 16000/ (1+r)³ - 18000/ (1+r)⁴ - 1000/ (1+r)⁵ = 0

r= Cross over Rate = 11.87 %

IRR_R = 18.26 %

IRR_S = 15.92 %

Requirement -2 :

PV at interest rate of 11.87%

NPV_R = NPV_S ( At Cross Over Rate) = $ 7720

Answer 2

1.
NPV of Project R=-55000+21000/(1+r)+22000/(1+r)^2+19000/(1+r)^3+12000/(1+r)^4+9000/(1+r)^5=7721.00678391295

2.
NPV of Project S=-76000+20000/(1+r)+20000/(1+r)^2+35000/(1+r)^3+30000/(1+r)^4+10000/(1+r)^5=7721.00678400605

3.
Crossover rate:
-55000+21000/(1+r)+22000/(1+r)^2+19000/(1+r)^3+12000/(1+r)^4+9000/(1+r)^5=-76000+20000/(1+r)+20000/(1+r)^2+35000/(1+r)^3+30000/(1+r)^4+10000/(1+r)^5

=>r=11.87%