Cost Of Capital

Here’s my stab at it – What do you think?

First compute WACC to find out the discount rate for the NPV using the information “Currently Didcot plc has 300,000 x £1 Ordinary shares and £200,000 of debt. The Ordinary Shareholders expect a yield of 17% and the after-tax cost of debt is 12%.”

WACC = (% equity x cost of equity) + (% debt x cost of debt)

= (.6 x .17) + (.4 x .12) = .15 or 15%

Next figure out the after tax cash flows for each prospective investment

Investment A has an immediate cash outflow of £50,000 and this would be followed by cash inflows of £20,000 at the end of year 1 and 2, £15,000 at the end of year 3 and 4.
For investment A, the initial outflow of £50,000 attracts a first year taxation capital allowance of 35% based on the initial investment amount, followed by writing down allowances of 35% of the tax written down value for years 2 and 3. As the investment will be disposed of at the end of year 4 with a nil residual value, the capital allowance to be claimed in year 4 will therefore be a balancing allowance which will reduce the taxation written down value to zero.
[For example if the initial investment had been £100,000, then capital allowances to be claimed would have been £35,000 in year 1, £22,750 for year 2, £14,788 for year 3 (tax written down value at this point = £100,000 – £72,538 = £27,462) and a balancing allowance of £27,462.]

Yr 0
-£50,000

Yr 1
£20,000 – cash flow

Yr 2
£20,000 – cash flow
£4,375 – tax savings due to capital allowance (W1)

Yr 3
£15,000 – cash flow
£2,844 – tax savings due to capital allowance (W1)

Yr 4
£15,000 – cash flow
£1,849 – tax savings due to capital allowance (W1)

Yr5
£3,433 – tax savings due to capital allowance (W1)

Then we discount the various cash flows to Yr 0 using the WACC of 15% computed previously

YR0 -£50,000
YR1 £17,391 (W2)
YR2 £18,431 (W2)
YR3 £11,733 (W2)
YR4 £9,633 (W2)
YR5 £1,707 (W2)

Adding these gives you the NPV for option A of £8,895

For option B the information given is:

Investment B requires no immediate cash outflow, but £5,000 per annum would be paid at the end of years 1, 2, 3 and 4. Cash inflows of £15,000 would also be received at the end of years 1, 2, 3 and 4.

For Investment B no capital allowances are available, but the annual outflows of £5,000 can be set against the £15,000 inflows for taxation purposes, making the taxable profits £10,000 per annum.

Yr0
£0

Yr1
+£15,000
-£5,000

Yr2
+£15,000
-£5,000
+£1,250 (Tax shield from previous year)

Yr3
+£15,000
-£5,000
+£1,250 (Tax shield from previous year)

Yr4
+£15,000
-£5,000
+£1,250 (Tax shield from previous year)

Yr5
+£1,250 (Tax shield from previous year)

Discount these flows back to year 0 using the WACC previously computed

Yr 0
Yr 1 £8,696
Yr 2 £8,506
Yr 3 £7,397
Yr 4 £6,432
Yr 5 £621

Adding these gives you the NPV for option B of £31,652

Option B should be selected in has a significantly higher NPV.

It is lower risk as it doesn’t involve a large initial investment.

The positive NPV is not dependent on the tax benefits related to the capital allowances which could be changed by the government in future budgets.

(W1)
For Year 1
£50,000 x .35 = £17,500
The initial cost times the capital allowance rate gives the capital allowance in £. Then tax rate is 25% so tax savings is:
£17,500 x .25 = £4,375
This isn’t actually used until year 2 as mentioned in the original question.

For Year 2 our asset balance is now £32,500 as it’s reduced by the capital allowance amount used in Y1 that’s what the question means by “writing down allowances of 35% of the tax written down value for years 2 and 3”

So we have
£32,500 x .35 = £11,375
Multiplied by the tax rate
£11,375 x .25 = £2,844

Yr 3 Asset balance is £50,000 – £17,500 – £11,375= £21,125

So we have
£21,125 x .35 = £7,394
Multiplied by the tax rate
£7,394 x .25 = £1,848

Yr 4 Asset balance is £50,000 – £17,500 – £11,375 – £7,394 = £13,731
For this year we can use the total asset value as an allowance against our taxes “the capital allowance to be claimed in year 4 will therefore be a balancing allowance which will reduce the taxation written down value to zero.”

So we have
£13,731 x .25 = £3,433

Hope this helps

Thank you very much for, rate for the capital allowance and WDA tax were the same.It should have been 35% for WDA tax and 25% for the capital allowance tax.