Questions:
Question 1
Zaha Ltd has an equity beta of 1.10. The market risk premium in South Africa is expected to be 5% and the yield on government bonds is currently 7.5%. Zaha has issued bonds and its R100 par-value bond is currently trading at R94.50. The coupon rate is 8%. The maturity date is in 5 years’ time and the corporate tax rate is 29%. Interest is payable annually in arrears. The company has just paid the coupon interest for the current year.
Required
- What is Zaha’s cost of equity, based on CAPM?
- What is the after-tax cost of debt?
- Zaha paid a dividend of R0.12 per share and the dividend per share is expected to grow at 7% indefinitely. The company’s share price is R2.30. What is the company’s cost of equity if we use the dividend growth model?
- What is the weighted-average cost of capital (WACC) if the target debt-equity ratio is 50%? (Use cost of equity as per CAPM)
Question 2
Afroflights wishes to make a takeover bid for Mayfly. Mayfly makes after-tax profits of R40 000 per year. Afroflights believes that if further money is spent on additional investments, the after-tax cash flows (ignoring the purchase consideration) could be as follows.
|
Year
|
Cash flow (net of tax)
R
|
|
0
|
(100 000)
|
|
1
|
(80 000)
|
|
2
|
60 000
|
|
3
|
100 000
|
|
4
|
150 000
|
|
5
|
150 000
|
The after-tax cost of capital of Afroflights is 15% and the company expects all the investments to payback, in discounted terms, within five years.
- What is the maximum price that the company should be willing to pay for the shares of Mayfly?
- What is the maximum price that the company should be willing to pay for the shares of Mayfly if it decides to value the business on the basis of cash flows in perpetuity, and annual cash flows from year 6 onwards are expected to be R120 000 with a sustainable growth rate of 6% per year?
Question 3
Amandla Pty is considering an investment in new technology that will reduce operating costs through increasing energy efficiency and decreasing pollution. The new technology will cost R1 million and have a four year life, at the end of which it will have a scrap value of R100 000.
A licence fee of R104 000 is payable at the end of the first year. This licence fee will increase by 4% per year in each subsequent year.
The new technology is expected to reduce operating costs by R5.80 per unit in current price terms.
Forecast production volumes over the life of the new technology are expected to be as follows:
|
Year
|
1
|
2
|
3
|
4
|
|
Production (units per year)
|
60 000
|
75 000
|
95 000
|
80 000
|
If Amandla bought the new technology, it would finance the purchase through a four-year loan paying interest at an annual before-tax rate of 8.6% per year. The loan repayment schedule is as shown in the table below:
Alternatively, Amandla could lease the new technology. The company would pay four annual lease rentals of R380 000 per year, payable in advance at the start of each year. The annual lease rentals include the cost of the licence fee.
If Amandla buys the new technology it can claim tax allowance depreciation on the investment on a 25% reducing balance basis. The company pays taxation one year in arrears at an annual rate of 30%. Amandla has an after-tax weighted average cost of capital of 11% per year.
Required
- Calculate and determine whether Amandla should lease or buy (using the loan facility) the new technology. (Round the discount rate and cash flows to zero decimal places)
- Using a nominal terms approach, calculate the net present value of buying (paying the full cost immediately) the new technology and advise whether Amandla should undertake the proposed investment.
Answers:
Question 1
The relevant formula for CAPM is given below.
Cost of Equity = Risk Free Rate + Beta* Market Premium
Based on the given question, risk free rate = 7.5%, beta =1.1 and market premium = 5%
Hence, cost of equity = 7.5 + 1.1*5 = 13% p.a.
Market value of bond = R94.50
Coupon rate =8% or (8/100)*100 = R8
Maturity period = 5 years
The YTM (Yield to Maturity) for the bond needs to be indicated by equation the current market price with the present value of expected future cash inflows. Based on the following table YTM comes out to be 9.43%
|
Year
|
Coupon Payment
|
Principal Repayment
|
Total cash inflows
|
PV ( R)
|
|
1
|
8
|
|
8
|
7.31
|
|
2
|
8
|
|
8
|
6.68
|
|
3
|
8
|
|
8
|
6.10
|
|
4
|
8
|
|
8
|
5.58
|
|
5
|
8
|
100
|
108
|
68.82
|
|
TOTAL
|
|
|
|
94.50
|
Post tax cost of debt = 9.43(1-0.29) = 6.7% pa
- Let the cost of equity be denoted by ke
In accordance with dividend growth model,
Price = Next Year Dividend /(Cost of equity – Growth rate of dividends)
Next year dividend = 0.12*1.07 = R 0.1284
Growth rate of dividends = 7% or 0.07
Price = R2.30
Hence, 2.30 = 0.1284/(ke – 0.07)
Solving the above, ke = 12.58% pa
It is apparent that if the debt equity ratio is 0.5, it implies that debt is 50% of equity.
Let equity be 2X
Then debt would be X
Weight of debt = (Debt/Debt +Equity) = (X/3X) = 33.33%
Weight of equity = (Equity/Debt +Equity) = (2X/3X) = 66.67%
WACC = weight of debt *cost tax cost of debt + weight of equity *cost of equity
WACC = 0.3333*6.7 + 0.6667*13 = 10.9% pa
Question 2
2.1 The maximum price that the company should be willing to pay would be equal to the NPV of the expected cashflows of Mayfly. This is computed in the table shown below.
|
Year
|
Cash flows
|
PV Factor
|
PV ( R)
|
|
0
|
-100000
|
1.00
|
-100000.0
|
|
1
|
-80000
|
0.87
|
-69565.2
|
|
2
|
60000
|
0.76
|
45368.6
|
|
3
|
100000
|
0.66
|
65751.6
|
|
4
|
150000
|
0.57
|
85763.0
|
|
5
|
150000
|
0.50
|
74576.5
|
|
Total
|
|
|
101894.5
|
Hence, the maximum price that the company could pay for Mayfly is R101,894.5
2.2 Now, the terminal value of the firm would also be added to determine the value of the Mayfly.
Terminal value at the end of year 6 = 120000*1.06/(0.15-0.06) = R 1,413,333
The NPV of the firm in the given case can be computed as follows.
|
Year
|
Cash flows
|
PV Factor
|
PV ( R)
|
|
0
|
-100000
|
1.00
|
-100000.0
|
|
1
|
-80000
|
0.87
|
-69565.2
|
|
2
|
60000
|
0.76
|
45368.6
|
|
3
|
100000
|
0.66
|
65751.6
|
|
4
|
150000
|
0.57
|
85763.0
|
|
5
|
150000
|
0.50
|
74576.5
|
|
6
|
120000
|
0.43
|
51879.3
|
|
6
|
1413333
|
0.43
|
611023.0
|
|
Total
|
|
|
764796.8
|
Hence, the maximum price that the company could pay for Mayfly is R764,796.8
Question 3
3.1 Upfront cost of buying = R1 million or R1,000,000
Scrap value at the end of 4 years = R 100,000
In case the company goes ahead and buy, the applicable depreciation in the four years can
Depreciation (Year 1) = (1000000-100000)*0.25 = R 225,000
Depreciation (Year 2) = (775000-100000)*0.25 = R 168,750
Depreciation (Year 3) = (606250 – 100000)*0.25 = R 126,563
Depreciation (Year 4) = (1000000-100000) –( 225000+168750+126563) = R 379,687
Applicable discount rate = 8.6(1-0.3) = 6% pa
Further, based on the given information, the NPV of buying the new technology is indicated below.
|
Year
|
0
|
1
|
2
|
3
|
4
|
|
Production (units)
|
|
60000
|
75000
|
95000
|
80000
|
|
Cost savings
|
|
348000
|
435000
|
551000
|
464000
|
|
(-) licence fee
|
|
104000
|
108160
|
112486
|
116986
|
|
(-) Depreciation
|
|
225000
|
168750
|
126563
|
379687
|
|
(-) Iniital investment
|
1000000
|
|
|
|
|
|
(+) Salvage value
|
|
|
|
|
100000
|
|
Incremental profit before tax
|
-1000000
|
19000
|
158090
|
311951
|
67327
|
|
Tax expense (@ 30%)
|
|
5700
|
47427
|
93585
|
20198
|
|
Earnings after tax ( R)
|
-1000000
|
13300
|
110663
|
218365
|
47129
|
|
(+) Depreciation
|
|
225000
|
168750
|
126563
|
379687
|
|
Net cash flows
|
-1000000
|
238300
|
279413
|
344928
|
426816
|
|
PV factor
|
1.00
|
0.94
|
0.89
|
0.84
|
0.79
|
|
PV cash flows ( R)
|
-1000000
|
224811
|
248677
|
289609
|
338078
|
|
NPV
|
101,175
|
The PV of cost for leasing the new technology is indicated below.
|
Year
|
Fee Paid
|
PV factor
|
PV ( R)
|
|
1
|
380000
|
1
|
380000
|
|
2
|
380000
|
0.90
|
342342
|
|
3
|
380000
|
0.81
|
308417
|
|
4
|
380000
|
0.73
|
277853
|
|
Total
|
|
|
1,308,612
|
The PV of benefits arising from leasing are indicated below.
|
Year
|
Savings
|
PV factor
|
PV ( R)
|
|
1
|
348000
|
0.90
|
313514
|
|
2
|
435000
|
0.81
|
353056
|
|
3
|
551000
|
0.73
|
402886
|
|
4
|
464000
|
0.66
|
305651
|
|
Total
|
|
|
1,375,107
|
NPV of leasing = 1375107-1308612 = $ 66,495
As the NPV associated with buying is more than that associated with leasing, hence the company would prefer to buy the concerned technology.
3.2 The NPV computation under the nominal terms method would deploy the discount rate as 11% and is indicated below.
|
Year
|
0
|
1
|
2
|
3
|
4
|
|
Production (units)
|
|
60000
|
75000
|
95000
|
80000
|
|
Cost savings
|
|
348000
|
435000
|
551000
|
464000
|
|
(-) licence fee
|
|
104000
|
108160
|
112486
|
116986
|
|
(-) Depreciation
|
|
225000
|
168750
|
126563
|
379687
|
|
(-) Initial investment
|
1000000
|
|
|
|
|
|
(+) Salvage value
|
|
|
|
|
100000
|
|
Incremental profit before tax
|
-1000000
|
19000
|
158090
|
311951
|
67327
|
|
Tax expense (@ 30%)
|
|
5700
|
47427
|
93585
|
20198
|
|
Earnings after tax ( R)
|
-1000000
|
13300
|
110663
|
218365
|
47129
|
|
(+) Depreciation
|
|
225000
|
168750
|
126563
|
379687
|
|
Net cash flows
|
-1000000
|
238300
|
279413
|
344928
|
426816
|
|
PV factor
|
1.00
|
0.90
|
0.81
|
0.73
|
0.66
|
|
PV cash flows ( R)
|
-1000000
|
214685
|
226778
|
252209
|
281157
|
|
NPV ( R)
|
-25,172
|
As the NPV of the project is negative, hence it should not be pursued.
