Question

Iron Ore Company Ltd. (IOC) is considering buying a new truck so that it can make its own deliveries. The truck will cost $150,000, has a life expectancy of five years and is expected to save the company $45,000 before tax each year in delivery expenses. IOC’s cost of capital is 9%, and its tax rate is 24%. Ignoring CCA and salvage, what is the payback period (PBP) and internal rate of return (IRR) for the proposed purchase? a) PBP = 3.33 years; IRR = 15.24% b) PBP = 4.39 years; IRR = 4.53% c) PBP = 4.39 years; IRR = 9.00% d) PBP = 5.83 years; IRR = 4.53%

Answer 1

Payback period = Cost of truck/Annual Savings after tax
= $150,000/45,000(1-0.24)

= 4.39 years

IRR is the rate at which NPV = 0

Let the IRR be x

0 = 45,000*(1-0.24)*PVAF(x%, 5 years) – 150,000

= 34,200*PVAF(x%, 5 years) – 150,000

PVAF(x%, 5 years) = 4.386

From Present value annuity factor table,

PVAF(4%, 5 years)= 4.4518

PVAF(5%, 5 years) = 4.3295

Using interpolation technique, IRR = 4% + (4.4518-4.386)/(4.4518 – 4.3295)

= 4.53%

Hence, the answer is b) PBP = 4.39 years; IRR = 4.53%