Question

QUESTION ONE:

Refer to the information provided below and answer the following questions:

1.1 Calculate the Payback period of the first alternative ( answer expressed in years, months and days)

1.2 Calculate the Accounting Rate of Return (on average investment) of the first alternative.

1.3 On the basis of the Net Present Value, which alternative should be chosen? provide relevant calculations (annuity discount factor @ 12% = 3.6048)

1.4 Calculate the internal Rate of Return of the first alternative (Annuity Discount Factor @ 13% = 3. 5 172)

information

The management of Woodies Incorporated is considering two investment opportunities:

- The first alternative involves the purchase of new machinery for R500 000 which will enable the company to modernise its plant. The machinery is expected to have a useful life of 5 years and no salvage value is anticipated. The modenisation is expected to increase effeciency, resulting in an increase of R142 000 in annual net cash flows.

- The second alternative involves purchasing a truck. the truck costs R500 000. its useful life is expected to be 5 years and a salvage value of R100 000 is anticipated. the truck is expected to generate R320 000 per year in additional revenues. The drivers salary and other cash operating expenses are expected to amount R180 000 per year. Woodies incorporated desires a return of 12%. the straight line method of depreciation is used.

Answer 1

Step 1: Arrive at Cash flows:

Alternative 1: Initial Investment is R500 000; Annual additional net cash flows is R142 000; There is no salvage value at the end of 5th year.

Alternative 2: Initial Investment is R500 000; Annual additional net cash flows is (R320 000 - R180 000) = R140 000; Salvage value at the end of 5th year is R100 000.

1.1. Payback Period for Alternative 1:

Payback period is the time required to recover the investments without considering the time value of money.

When Annual Cash flow is equal, then Payback Period = Initial Investment / Annual Cash flow

Payback period for Alternative 1 = R500 000 / R142 000 = 3.52 Years i.e 3 years, 6 months and 7 days (Approx)

1.2. Accounting Rate of Return of Alternative 1:

Accounting Rate of Return is the ratio of average income to the investment made. Time value of money is also not considered here.

Accounting Rate of Return = Average net profit / Average Investment

Depreciation per year = R500 000/5 years = R100 000

Annual Net profit = R142 000 - R100 000 = R42 000

(Since the cash flows and depreciation is same in all the years, average net profit = annual net profit)

ARR = R42 000 / R500 000 = 0.084 = 8.4%

1.3. Decision making based on Net Present Value:

Net Present Value (NPV) is the difference between Present value of Cash inflows and present value of Cash outflows. It takes into account the Time Value of Money.

NPV = Present value of Cash inflows - Present value of Cash outflows

Present value of cash flow of 1 year = Cash flow / (1+rate)^year

When Annual Cash flows are equal then Present Value of all cash flows which are equal is obtained by multiplying the annual cash flow with annuity discount factor.

Annuity Discount Factor @ 12% is 3.6048

NPV of Alternative 1:

Present Value of Cash inflows = R 142 000 * 3.6048 = R511 881.60

Present Value of Cash outflows = Initial Investment = R500 000

NPV = R511 881.60 - R500 000 = R11 881.60

NPV of Alternative 2:

There is a cash inflow in the 5th year in the form of salvage value of asset, hence Present value of the same needs to be computed separately.

Present Value of Cash Inflows (Equal Cash flows) = R140 000 * 3.6048 = R504 672

Present Value of Cash inflow at the end of 5th year (Salvage Value) = Cash flow / (1+rate)^year = R100 000/(1+0.12)⁵ = R56 742.69

Total Present Value of Cash Inflows = R504 672 + R56 742.69 = R561 414.69

Present Value of Cash outflows = Initial Investment = R500 000

NPV = R561 414.69 - R500 000 = R61 414.69

Since the net present value of Alternative 2 is higher than that of Alternative 1, Alternative 2 should be chosen.

1.4. Internal Rate of Return of Alternative 1:

Internal Rate of Return (IRR) is a rate at which the NPV of any project or investment is zero.

IRR is obtained using a trial & error method. However when 2 NPV's are obtained at different Discount rates, IRR can be obtained using the following method:

Annuity Discount Factor @ 13% = 3.5172

NPV at 12% as calculated earlier = R11 881.60

NPV at 13% = (R142 000 * 3.5172) - R500 000 = R -557.60

Change in NPV = NPV at lower rate - NPV at higher rate / difference of rates

= [R11 881.60 - (R-557.60)] / 13-12 = (R11 881.60 + R557.60)/1 = 12 439.20

Increase of Percentage points from 12% = NPV @ 12% / 12 439.20 = 11 881.60 / 12 439.20 = 0.9552

IRR = Lower Rate + Increase in percentage points = 12 + 0.9552 = 12.9552%