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Question 1
Zaha Ltd’s equity beta is 1.10.
The market risk premium for South Africa is expected at 5%, and the yield on government bonds currently stands at 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 within 5 years and the corporate tax rate at 29%.
In arrears, interest is payable each year.
The coupon interest has been paid by the company for the current fiscal year.
Requirements
Based on CAPM, what is Zaha’s equity cost?
What is the cost of debt after taxes?
Zaha paid R0.12 per share in dividends. The dividend per share will continue to grow at 7% annually.
The share price of the company is R2.30.
How much equity does the company have if it uses the dividend growth model to calculate?
If the target debt-equity ratio for a company is 50%, what is the weighted average cost of capital (WACC).
(Use cost-of-equity as per CAPM
Question 2
Afroflights is interested in making a takeover offer for Mayfly.
Mayfly earns after-tax profits of R40000 per year.
Afroflights believes that additional money can be spent on investments to increase cash flow after taxes, ignoring purchase consideration.
Year
Cash flow (net tax)
R
Afroflights’ after-tax capital cost is 15%. The company expects all investments to be repaid in discounted terms within five years.
What should the maximum price be paid by Mayfly for its shares?
Is there a maximum price the company should pay for Mayfly shares if it values the business on cash flows in perpetuity? Annual cash flows starting at R120 000 and a sustainable growth rate above 6% are the expected cash flows.
Question 3
Amandla Pty plans to invest in new technology that will lower operating costs, increase energy efficiency, and reduce pollution.
The new technology will be R1 million in cost and will last for four years. At the end it will have a value of R100 000.
At the end of the first calendar year, a R104 000 licence fee is due.
In each subsequent year, the licence fee will go up by 4%.
In current price terms, the new technology will reduce operating costs by R5.80 an unit.
The following are the expected production volumes for the lifetime of the new technology:
Year
Production (units/year)
Amandla could finance the purchase of the new technology by taking out a 4-year loan at 8.6% interest per annum.
Below is the loan repayment schedule:
Amandla could also lease the technology.
The company would be responsible for four annual lease rentals totalling R380 000 each year. These rents are payable in advance at each year’s beginning.
The cost of the license fee is included in the annual lease rental.
Amandla can claim 25% tax allowance depreciation if she purchases the new technology.
The company pays 30% annual tax arrears for one year.
Amandla’s average after-tax capital cost is 11% per annum.
Requirements
Calculate the cost of the new technology and decide if Amandla should buy or lease it (using the loan facility).
(Round the cash flows and discount rate to zero decimal places.
Calculate the net present value (or the cost of purchasing the entire new technology immediately) using nominal terms and recommend to Amandla whether the proposed investment should be made.
Question 1
Below is the relevant formula for CAPM.
Cost of Equity = Risk-Free Rate + Beta*Market Premium
Based on the question, risk-free rate = 7.5%, beta=1.1, and market premium = 5.5%
Cost of equity = 7.5 + 1. *5 = 13%
Bond par value = R100
Market value of bond = R94.50
Coupon rate =8%, (8/100)*100 =R8
Period of maturity = 5 years
The YTM (Yield To Maturity) of the bond must be calculated by dividing the current market price and the expected future cash inflows.
The following table shows that YTM is 9.43%
Year
Coupon Payment
PV ( R).
TOTAL
6.7% pa after tax cost of debt = 9.43 (1-0.29).
Let us denote the cost of equity by ke
According to the dividend growth model
Price = Next Year Dividend/(Cost Equity – Growth Rate of Dividends)
Next year dividend = 0.12*1.07 = Rs 0.1284
Dividend growth rate = 7% or 0.07
Price = R2.30
Solving the above equations, ke = 12.58% Pa
It is obvious that 50% of equity is represented by debt if the debt equity ratio equals 0.5.
Equity should be 2X
Then, the 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 + 0.667*13 = 10.9%
Question 2
2.1 The company should not be willing to pay more than the NPV for Mayfly’s expected cashflows.
The table below shows how this calculation is done.
Year
Cash flows
PV Factor
PV ( R).
Total
Therefore, Mayfly’s maximum price is R101,894.5
2.2 The terminal value of the firm will also be added to determine value of Mayfly.
In the following example, you can calculate the NPV for the firm.
Year
Cash flows
PV Factor
PV ( R).
Total
Therefore, Mayfly’s maximum price is R764,796.8
Question 3
3.1 Initial cost of purchase = R1,000,000 or R1,000,000
R 100,000 is the scrap value at the end after 4 years.
If the company decides to buy, the depreciation applicable over the next four years will be applied.
Further, the following information shows the NPV for purchasing the new technology.
Year
Production (units).
Cost savings
(-) Licence fee
(-) Iniital investments
Incremental profit before taxes
Net cash flows
PV factor
PV cash flows (R)
Below is the PV of cost for leasing new technology
Year
Fee Paid
PV factor
PV ( R).
Total
Below are the PV of Benefits Associated With Leasing
Year
Save!
PV factor
PV ( R).
Total
Leasing NPV = 1375107-1308612 = $66,495
The NPV associated to buying technology is higher than that associated leasing. Therefore, the company would rather buy it.
3.2 In nominal terms, the NPV calculation would use the 11% discount rate and is shown below.
Year
Production (units).
Cost savings
(-) Licence fee
(-) Initial investment
Incremental profit before taxes
Net cash flows
PV factor
PV cash flows (R)
NPV ( R).
The project’s NPV is negative so it shouldn’t be pursued.
