Question

1. Cooper Copper Company is considering the purchase of two new molding machines. Machine A and Machine B both have a cost of $10,000 and will be evaluated using a 12% cost of capital. The machines’ expected net cash flows are as follows: Expected Net Cash Flows Year Machine A Machine B 0 -$10,000 -$10,000 1 6,500 3,500 2 3,000 3,500 3 3,000 3,500 4 1,000 3,500 a. Calculate each project’s payback period. b. Calculate each project’s discounted payback period. c. Calculate each project’s net present value (NPV). d. Calculate each project’s internal rate of return (IRR). e. Calculate each project’s profitability index (PI). f. Which project(s) should be accepted if they are independent? Explain. g. Which project should be accepted if they are mutually exclusive? Explain.

Please break down step-by-step in Word or notepad.

Answer 1

a). Payback period is the period in which the cashinflows will cover the initial investment

For Machine A, First 2 years cashinflows is 6500+3000= 9500. Remaining 500 can be achieved in 500/3000= 0.166th of third year. So, Payback period= 2.166 Years.

For Machine B, First 2 years cashflows is 3500+3500= 7000. Remaining 3000 can be achieved in 3000/3500= 0.857 th of third year. So, Payback period= 2.857 Years

b). Discounted Payback period is the period in which the discounted cashinflows will cover the initial investment.

For Machine A, First 2 years discounted cashflows is 6500/(1.12)+3000/(1.12)^2= 8195.15. Remaining 10000-8195.15= 1804.85 can be achieved in 1804.85/(3000/1.12^3)= 0.845 th of third year. So, Payback period= 2.845 Years.

For Machine B, First 3 years discounted cashflows is 3500/(1.12)+3500/(1.12)^2+3500/1.12^3= 8406.41. Remaining 10000-8406.41= 1593.59 can be achieved in 1593.59/(3500/1.12^4)= 0.716 th of fourth year. So, Payback period= 3.716 Years

c). NPV for a time period of n can be calculated using the formula: -C+C1/(1+r)+C2/(1+r)^2+....Cn/(1+r)^n; where C is the initial investment, C1 to Cn are cash inflows and r is the required rate of return

For Machine A, NPV= -10000+6500/1.12+3000/1.12^2+3000/1.12^3+1000/1.12^4

= $966.01

For Machine B, NPV= -10000+3500/1.12+3500/1.12^2+3500/1.12^3+3500/1.12^4

= $630.72

d). IRR is the discount rate at which NPV is 0.
Let IRR be r, then C+C1/(1+r)+C2/(1+r)^2+....Cn/(1+r)^n= 0.

For Machine A, IRR will be at

-10000+6500/(1+r)+3000)(1+r)^2+3000/(1+r)^3+1000/(1+r)^4= 0.

On Solving, r is 18.032%

For Machine B, IRR will be at

-10000+3500/(1+r)+3500/(1+r)^2+3500/(1+r)^3+3500/(1+r)^4= 0.

On Solving, r is 14.963%

e). Profitability Index is calculated using the formula 1+(NPV/Initial Investment)

For Machine A, PI= 1+(966.01/10000)= 1.0966

For Machine B, PI= 1+(630.72/10000)= 1.063

f). If the projects are independent, we need to choose the projects whose NPV is greater than zero. So, we choose both Machine A and Machine B.

g). If the projects are mutually exclusive, we need to select the project whose NPV is greater. So, we choose Machine A.