Question

A major new client has requested your company to present an investment seminar to the municipal mayors of the represented Metros. As an investment specialist, you have been tasked to assist your company in preparing the presentation. To illustrate the common share valuation process, you have been asked to analyze Business Analytics, an employment agency that supplies word processor operators and computer programmers to businesses with temporarily heavy workloads. You are to answer the following:

2.1 Assume that Business Analytics has a beta coefficient of 1.2, that the risk-free rate ( the yield on T-bonds) is 3%, and that the required rate of return on the market is 8%. What is Business Analytic's required rate of return?

2.2 Assume that Business Analytics is a constant growth company whose last dividend (D0, which was paid yesterday) was R2.00 and whose dividend is expected to grow indefinitely at a 4% rate.

i. What is the company's expected dividend stream over the next 3 years?

ii. What is its current share price?

iii. What is the share's expected value 1 year from now?

2.3 now assume that the share is currently selling at R40.00. What is its expected rate of return?

2.4 What would the share price be if its dividends were expected to have zero growth?

2.5 Now assume that Business Analytics'dividend is expected to grow at 30% in the first year, 20% in the second year, 10% in the third year, and return to its long-run constant growth rate of 4%. What is the share's value under these conditions?

2.6 Suppose Business Analytics' is expected to experience zero growth during the first 3 years and then resume its steady-state growth of 4% in the fourth year. What would be its value then?

2.7 Finally, assume that Business Analytics' earnings and dividends are expected to decline at a constant rate of 4% per year, that is, g=-4%. Why would anyone be willing to buy such a share, and at what price should it sell?

2.8 suppose Business Analytics' embarked on an aggressive expansion that requires additional capital. Management decided to finance the expansion by borrowing R40 million and by halting dividend payments to increase retained earnings. Its WACC is now 7% and the projected free cash flows for the next three years are -R5 million, R10 million, and R20 million respectively. After Year 3, free cash flow is projected to grow at a constant 5%. What is Business Analytics' market value of operations? If it has 10 million shares, R40 million of debt and preferred share combined, and R5 million of non-operating assets, what is the price per share?

2.9 Suppose Business Analytics decided to issue preferred share that would pay an annual dividend of R5.00 and that the issue price was R100.00 per share. What would be the share's expected return? Would the expected rate f return be the same if the preferred share was a perpetual issue or if it had a 20-year maturity?

Answer 1

2.1:

Required rate of return=  Risk free rate + Beta(Market risk-risk free rate)

= 3%+1.2(8%-3%)

=9%

2.2:

i) Company's expected dividend stream for next 3 years:

Year 1= 2*1.04= R2.08

Year 2= 2.08*1.04= R2.1632

Year 3= 2.1632*1.04= R2.249

ii) Current share price:

Formula- D1/ (r-g),

where,

D1= Dividend of next year

r= rate of return

g= growth

Therefore, Current share price= (2*1.04)/ (9-4)= R41.6

iii) Share's expected value 1 year from now:

P1= D2/r-g

where,

P1= Price of 1 year from now,

D2= Dividend of 2 years from now

Therefore,

P1= (2.08*1.04)/(9-4)= R43.264

2.3:

If share is currently selling at R40,

Expected rate of return i.e. "r" = [(D1/P0)+g

Where,

D1 = 2*1.04=2.08

P0= 40

g= 1.04

Therefore, expected rate of return= [(2.08/40)+1.04]= 9.2%

2.4:

If the dividend has 0 growth,

And rate of return is 9%

Share price= 2/9% = R22.22

2.5:

Dividend growth in first year: 30%

Dividend growth in second year: 20%

Dividend growth in third year: 10% in the third year,

After 4^th year: constant growth rate of 4%.

Calculation of Current share price is as follows:

Year	Dividend	Discounting factor'	Present Value
0	2	1	2*1=2
1	2*1.3=2.6	1/1.09= .917	2.6*.9174=2.3853
2	2.6*1.2=3.12	1/1.09^2=.8417	3.12*.8417=2.626
3	3.12*1.1=3.432	1/1.09^3=.7722	3.432*.7722=2.6501
4	3.432*1.04=3.569	1/1.09^4=.7084	3.569*.7084=2.5286
After 4th year	3.56928*1.04=3.712	1/((9%-4%)*1.09^5)= 12.9986	3.712*12.9986=48.2516
		Current Share price	R60.4416

2.6:

If zero growth during the first 3 years and then steady-state growth of 4% in the fourth year,

Then

Share value shall be computed as follows:

Year	Dividend	Discounting factor'	Present Value
0	2	1	2*1=2
1	2	1/1.09= .917	2*.9174=1.835
2	2	1/1.09^2=.8417	2*.8417=1.684
3	2	1/1.09^3=.7722	2*.7722=1.545
4	2*1.04=2.08	1/1.09^4=.7084	2.08*.7084=1.474
After 4th year	2.08*1.04= 2.1632	1/((1.09-1.04)*1.09^5)= 12.9986	2.1632*12.9986=28.119
		Current Share price	36.657