Houston Corporation is considering an investment in equipment for £45,000. Data related to the investment are as follows: Cost of capital is 18 percent.
Houston claims capital allowances (WDV's) using the straight-line method of depreciation . In addition, their tax rate is 40 percent, and the life of the equipment is five years with no salvage value.
What is the net present value of the investment?

Question

Quizplus · Accepted Answer

First, we need to calculate the annual depreciation using the straight-line method:

Annual depreciation = (Cost of equipment - Salvage value) / Life of equipment
Annual depreciation = (£45,000 - £0) / 5 years
Annual depreciation = £9,000

Next, we can calculate the annual cash inflows using the following formula:

Annual cash inflows = (Annual net income + Annual depreciation) x (1 - Tax rate)

Since there is no salvage value, the annual net income will be equal to the annual depreciation:

Annual net income = Annual depreciation = £9,000

Therefore, the annual cash inflows will be:

Annual cash inflows = (£9,000 + £9,000) x (1 - 0.40)
Annual cash inflows = £10,800

To calculate the net present value (NPV), we need to discount the annual cash inflows back to their present value using the cost of capital. We can use the following formula:

NPV = - Cost of equipment + SUM (Annual cash inflows / (1 + Cost of capital)^n)

Where n = the year of the cash inflow (i.e. Year 1, Year 2, etc.)

Using a discount rate of 18 percent, the present value of the annual cash inflows is:

Year 1: £10,800 / (1 + 0.18)^1 = £9,153
Year 2: £10,800 / (1 + 0.18)^2 = £7,766
Year 3: £10,800 / (1 + 0.18)^3 = £6,600
Year 4: £10,800 / (1 + 0.18)^4 = £5,618
Year 5: £10,800 / (1 + 0.18)^5 = £4,790

Therefore, the net present value is:

NPV = -£45,000 + (£9,153 + £7,766 + £6,600 + £5,618 + £4,790)
NPV = £22,543

Since the NPV is positive, the investment is expected to generate a return that exceeds the cost of capital, and Houston Corporation should proceed with the investment.

Houston Corporation Is Considering an Investment in Equipment for £45,000