Question

Advanced Automation LLC is a recently listed company. The shareholders in this company have just received a dividend payment and they have been told that their next dividend payment will be $2.78. Investors expect this dividend to grow at constant rate of 3% pa thereafter. Assume that the required return for the investor is 13% pa.

a)Calculate the value of the company's share immediately after the dividend payment. Give your answer in dollars and cents to the nearest cent.

Value of share = $

Immediately after the dividends were paid, Advanced Automation LLC suddenly lost a key competitor who was involved in a huge corporate scandal. Investors believe that the resultant increase in market share will make the dividends grow faster than they initially predicted. They predict that the dividend growth will be increased to a constant rate of 5%.

b)Assuming the required return is the same as previously, calculate the increase in the value of the share caused by losing their key competitor. Give your answer in dollars and cents to the nearest cent.

Increase in value of share = $

2. Southern Infrastructure Corporation's last dividend payment was $1.98. The company's cost of equity funds is 16.9% pa and its expected future dividend growth rate is 4.7% pa. Using the constant dividend growth model, calculate Southern Infrastructure Corporation's share price (P). Give your answer in dollars and cents to the nearest cent.

P = $

3. A bond with a face value of $1,800 pays half-yearly interest at a rate of 6% pa compounded half-yearly and has 7 years until maturity. The next interest payment is due in exactly one half-year. Calculate the price (P) required to yield 4% pa compounded half-yearly. Give your answer in dollars and cents to the nearest cent.

P = $

4. Calculate the purchase price of the following bonds. Indicate whether the bonds are priced at a discount, at par or at a premium. Give your answers in dollars and cents to the nearest cent.

	Face Value	Coupon Rate	Years to Maturity	Market Rate
a)	$100	r = 10.75%	4	j2 = 12.5%
b)	$1,000	r = 7%	11	j2 = 7%
c)	$10,000	r = 6.75%	21	j2 = 5%

Quoted coupon rates and market rates are nominal annual rates compounded semi-annually.

a)Price = $

This bond is priced at:

a discount
par
a premium

b)Price = $

This bond is priced at:

a discount
par
a premium

c)Price = $

This bond is priced at:

a discount
par
a premium

5. Biti Bank purchase a $4,000 bond that pays 9% pa compounded half-yearly and is redeemable in exactly 10 years. The price paid will yield the bank 5% pa compounded half-yearly if held to maturity. Biti Bank hold this bond for 6 years before coming to a decision that the bond should be sold. They decide to sell to ZNZ Bank at 4.4% pa compounded half-yearly.

a)Calculate the price (P_B) that Biti Bank paid to purchase the bond. Give your answer in dollars and cents to the nearest cent.

P_B = $

b)Calculate the price (P_Z) that ZNZ Bank paid to purchase the bond. Give your answer in dollars and cents to the nearest cent.

P_Z = $

c)Calculate the nominal annual yield compounded half-yearly that Biti Bank realised. You may give your answer as a percentage per annum to the nearest percent or use linear interpolation or a financial calculator to give a more accurate result.

Yield =  % pa

6.You are thinking about investing in Suzie's Super Speakers. You notice the following newspaper article about the business:

When asked about the future of her successful company, Suzie highlighted that her company had paid dividends of $0.70 last year, and are due to pay dividends again today. Suzie is excited because today's dividends will be 4.3% higher than last year's. Suzie has spent years slowly raising her dividends to this level but now expects to maintain dividends at today's level for the life of her business. Suzie's Super Speakers currently return 12.1% pa to shareholders.

Based on this information, calculate the share price (P) for Suzie's Super Speakers immediately after today's dividends are paid. Give your answer in dollars and cents to the nearest cent.

P = $

Answer 1

1a). The next dividend payment will be $2.78 and after that, dividends will grow at a rate of 3% for perpetuity.

The first dividend in perpetuity D_p1 = 2.78*(1+3%) = 2.8634

Terminal value of dividends (TV) = D_p1/(k-g)

where k = required rate of return of investors = 13% and g = growth rate of dividends = 3%

TV = 2.8634/(13%-3%) = 28.634

This is the TV at the end of t = 1 along with the dividend payment of 2.78 at t = 1.

Discount both at k, to t = 0:

Current share price = 2.78/(1+13%)^1 + 28.634/(1+13%)^1 = $27.8

1b). Now, immediately after the dividend is paid, the new perpetual growth rate of the company is forecasted to be 5%.

New D_p1 = 2.78*(1+5%) = 2.919

New TV = D_p1/(k-g) = 2.919/(13%-5%) = 36.4875

Again, discounting from t = 1 to t = 0:

Current share price = 2.78/(1+13%)^1 + 36.4875/(1+13%)^1 = 34.8

Increase in value of share price = 34.8 - 27.8 = $7.0

2). Last dividend payment = 1.98

Perpetual dividend growth rate g = 4.7%

First dividend in perpetuity Dp1 = 1.98*(1+4.7%) = 2.07

Cost of equity k = 16.9%

As per the constant growth model, current share price = Dp1/(k-g) = 2.07/(16.9%-4.7%) = $16.99 or $17.0