Question

(Ignore income taxes in this problem.) Allen Company's required rate of return is 14%. The company is considering the purchase of a new machine that will save $10,000 per year in cash operating costs. The machine will cost $40,000 and will have an 8-year useful life with zero salvage value.

Required:

i） Compute the machine's internal rate of return to the nearest whole percent. Would you recommend purchase of the machine? Explain.

ii)     The company would like to use NPV to evaluate the project now. Compute the machine's NPV, assuming cost of capital is 10%. Would you recommend purchase of the machine? Explain.

iii) Discuss the implications for project investment priority based on your answer in (i) and (ii).

Answer 1

SOLUTION :

I)

Initial  cash flow = - $40000 

Annual savings = $10000 for 8 years.

Salvage value at the end off 8 years = 0

rate of return required = 14% =m0.14

At IRR, NPV = 0 . Let IRR be r in decimals. Cash flows will be discounted at this rate.

So, 

NPV = 0 = - 40000 + 10000((1 + r)^8 - 1)/(r(1+r)^8) 

By trial and error, r = IRR = 0.186237 = 0.1862 approx. = 18.62% 

As IRR (18.62%) > required rate of return of 14%, machine should be purchased.

(ANSWER)

ii)

Discount rate , k = Cost of capital = 10% = 0.10 .

=> (1 + k) = 1.10 .

NPV = - 40000 + 10000(1.10^8 - 1)/(0.10*1.10^8)

=> NPV = 13349 ($)

As NPV is positive, machine should be purchased. (ANSWER).

iii)

As per (I) and (ii) , both, investment in buying machine is recommended. 

(ANSWER).