You are interested in purchasing a shoe machine XYZ, especially designed for men

Question

You are interested in purchasing a shoe machine XYZ, especially designed for men's fashion shoes. The machine costs $10,000. You expect to recover $6,000 a year in operating cash flows for only two years because of rapidly changing fashions. You estimate the salvage value of the machine at the end of two years to be $1,200. Assume that the tax rate is zero. Assume that the $6,000 per year after tax operating cash flow is received at the end of each year.

a) What is the Net Present Value (NPV) of this project, if cash flows are to be discounted at 20% cost of capital?

(b) What is the IRR of this project?

You decide to invest in machine XYZ. But just before you place an order for the machine you hear about another machine UVW. This machine costs $15,000 and has operating flows of $18,000 during the first year and, for some unknown reason, only $50 during the second year, with no salvage value at the end of two years. (Assume all cash flows occur at the end of the year for the purpose of discounting.)

(c) You know that whether you prefer XYZ or UVW depends upon your cost of capital. Draw the graph showing how NPVs of these two machines relate to their cost of capital. Both NPVs should be on the same graph.

(d) At what cost of capital both machines have the same Net Present Value? (Please do not forget to show the equation you need to solve with the help of Excel to answer this question).

(e) What is the IRR of machine UVW?

PLEASE SHOW ALL FORMULAS AND CALCULATIONS. THANK YOU.

Explanation / Answer

a)
Calculate the NPV of the XYZ machine:
Year   Cash flows   Discounting
factor @ 20%   Discounted
cash flows
0   $ (10,000)   1.00000   $ (10,000.00)
1   $ 6,000    0.83333   $ 4,999.98
2   $ 6,000    0.69444   $ 4,166.64
2   $ 1,200    0.69444   $ 833.33
    NPV   $ (0.05)

Therefore, NPV of the XYZ machine is - $0.05

b)
Calculate the IRR of XYZ machine:
IRR = (cash flow year 1 / (1 + IRR)1) + (cash flow year 2 / (1+IRR)2) – Initial investment
= ($6,000 /(1+ IRR)1) + ($7,200 / (1+IRR)2) – $ $10,000
= 20%

Therefore, IRR is 20%.

C) and d)
Calculation NPV of UVW machine:
Year   Cash flows   Discounting
factor @ 20%   Discounted
cash flows
0   $ (15,000)   1.00000   $ (15,000.00)
1   $ 18,000    0.83333   $ 14,999.94
2   $ 50    0.69444   $ 34.72
    NPV   $ 34.66

Therefore, NPV is $34.66.

e)
Calculate the IRR of UVW:
IRR = (cash flow year 1 / (1 + IRR)1) + (cash flow year 2 / (1+IRR)2) – Initial investment
= ($18,000 /(1+ IRR)1) + ($50 / (1+IRR)2) – $ $15,000
= 20.2772%

Therefore, IRR of UVW is 20.2772%.

f)
Machine UVW is better than XYZ due to it has positive NPV and higher IRR of XYZ machine.

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