Question

14. Morrison Vans is considering the purchase of a new vehicle to replace an old one. The old vehicle originally cost $40,000, but has been fully depreciated and now has a current market value and book value of zero. It is estimated that the proposed new vehicle generates efficiencies and savings of $16,000 per year before tax. The new vehicle costs $60,000 delivered and installed, and its economic life is estimated to be ten years with no salvage value. Morrison's cost of capital is 14% (discount rate); depreciation is on a straight-line basis; and the total corporate tax rate is 40%. a. What is the Payback Period for the investment in the new vehicle? b. What is the Net Present Value (NPV) of the investment in the new vehicle? c. What is the Internal Rate of Return (IRR) of the new vehicle? d. What is the Profitability Index (PI) of the investment?

Answer 1

New Machine Initial Cost = $60,000

Useful life of new machine = 10 years

Annual Depreciation = 60000/10 = $6,000

Annual before tax saving = $16,000

Tax rate = 40%

Discount rate = 14%

Thus,

After tax Annual cash flow from new machine:

$\dpi{100} = 16000*(1-0.4)+6000*0.4$

$\dpi{100} = \$12,000$

a. Payback Period

$\dpi{100} = \frac{\textup{Initial Cost}}{\textup{Annual after tax cash flow}}$

$\dpi{100} = \frac{60,000}{12,000}$

$\dpi{100} \bg_green \large =\textup{ 5 years}$

b. Net Present Value (NPV) :

$\dpi{100} = ATCF*(P/A,0.14,10)-\textup{Initial Cost}$

$\dpi{100} = 12,000*(P/A,0.14,10)-60,000$

$\dpi{100} = 62,593.39-60,000$

$\dpi{100} \bg_green \large = \$2,593.39$

c. Suppose, IRR = r

At IRR rate NPV of machine would be zero.

Thus,

$\dpi{100} 0 = 12,000*(P/A,r,10)-60,000$

by solving using trial and error method,

$\dpi{100} \bg_green \large r = 15.10\%$

d. Profitability Index(PI)

$\dpi{100} = \frac{\textup{PV of Cash Inflows}}{\textup{PV of Cash Outflows}}$

$\dpi{100} = \frac{62,593.39}{60,000.00}$

$\dpi{100} \bg_green \large = 1.04$

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.