Question

[Answer with True (T) or False (F)]

1. For the dividend discount model (DDM) under supernormal growth (or non-constant
growth model), the discount rate (r) during the initial supernormal growth period is as
same as the discount rate (r) used in the later, steady growth period. ( )

2. For the corporate valuation model (or free cash flow (FCF) discount model) in firm
valuation, the cost of common equity (rc) is generally used as a discount rate. ( )

3. If the expected return of a stock based on the current stock price (P0) is located above
the security market line (SML), then a stock analyst would issue a coverage report with
a “buy” recommendation. ( )

4. If the internal rate return (IRR) and the net present value (NPV) methods give
conflicting results between mutually exclusive projects, the project with a higher NPV
should be chosen. ( )

Choose a correct statement among the following options regarding stock valuation.
( )

1 The dividend discount model under steady growth is a suitable model for a newly-
listed technology firm expected to undergo a stable growth phase in 5 to 10 years.

2 For a stock with a 12% required return, if the dividend payout is expected to grow
steadily at 5% (g=5%), the expected dividend yield in the following year is also
5%.
3 Even when a negative dividend growth is expected, a constant-growth dividend
discount model (P0 =
D1
(rs−g)
) can be used.

4 The intrinsic value of a stock is the total discounted value of all future expected
dividend payouts using the dividend growth rate (g) as the discount rate.

5 For a firm with zero expected growth of dividend, the dividend discount model
under constant growth cannot be used.

6. Choose a wrong statement regarding capital budgeting. ( )
1 For a business project with a negative net present value (NPV), its internal rate of
return (IRR) must be lower than the weighted average cost of capital (WACC)
used to evaluate the project.
2 Because the NPV and IRR of mutually exclusive projects can give opposite results,
entirely depending on the IRR method to choose a business project can minimize
the risk of misjudgment.
3 The big difference between the NPV and IRR methods lies on the assumption
regarding the reinvestment of cash flows during the investment periods.
4 The IRR and NPV methods always give the same results for independent projects.

The risk of stocks can be measured in two types: First, a stand-alone risk, the risk an
investor would face if he or she held only one asset which can be represented by the
variance or standard deviation. Second, a systematic risk, the risk that remains on a
portfolio after diversification has eliminated all company-specific risk which can be
measured by the beta. The capital asset pricing model (CAPM) uses the beta to estimate
the required return to investing a stock.
(1) Calculate the required return to SUNNY Inc.’s stock given that the risk-free rate
is at 5%, the market risk premium is at 3% (or the expected market return at 8%),
and the beta of SUNNY, Inc. is at 1.2. (3 points)

(2) SUNNY, Inc., paid a $10/share dividend in the last fiscal period and its net profits
are expected to grow at 5%. How much should SUNNY, Inc.’s stock trade per
share? (3 points)

SUNYK, Ltd. plans to payout a $1 per share dividend at the end of this fiscal period.
The dividend is expected to constantly grow at 5% per period. SUNYK’s required
return is 10% and the company currently trades at $22 per share. Please recommend
your investors for a decision among “hold”, “buy”, or “sell” and give your reasoning.
(5 points)

10. Stony Brook Corp. recently paid an annual $15 per share dividend. From the recently
approved patent, this company’s net profits will grow at 20% in the next 2 years, and
at 5% in the third year and beyond due to expiration of the patent. The required return
to this company’s shareholders is at 10%.
(1) Calculate the intrinsic value of Stony Brook’s stock per share. (4 points)

(2) Calculate the dividend yield and the capital gains yield for the first year (t=0).
Round up to the first decimal point if your answer is expressed in percentage (%)
(or up to the third decimal point if written in fraction). (4 points)

(3) Calculate the dividend yield and the capital gains yield for the third year (as at the
beginning of the third year (t=2)). Round up to the first decimal point if your
answer is expressed in percentage (%), or up to the third decimal point if written
in fraction. (4 points)

(4) What is the expected stock price of this company in five years? Round up to the
second decimal point. Provide all your calculation for partial points. (4 points)

There a project for SBU, Inc. with expected cash flows describe below.

Answer the following questions with the additional information give below. (25 points
total)

◼ Tax rate = 40%
◼ Capital structure

◼ Debt: Face value at $1,000; 10 years of maturity; 10% semiannual coupons;
price $885.30; no addition cost of new debt issuance.
◼ Preferred stock: $10 annual dividend per share; price $111.10.
◼ Common stock:
‧ Price $42; dividend payout (D0) at $4 per share; steady growth of net
profits expected at 5% per year
‧ Beta at 1.3; risk-free rate (rf) at 8%; market risk premium at 6%
‧ For illiquid (infrequently traded) stocks, 3-5% bond-yield risk premium
is added to the long-term bond yield.

(1) Calculate the cost of debt capital (before and after tax) assuming no floatation
costs. (3 points)

(2) Calculate the cost of preferred stock assuming no floatation costs. (3 points)

(3) Calculate the cost of common stock assuming no floatation cost.
i. Use the dividend discount model (DDM) under steady growth (Gordon model).
(3 points)

ii. Use the capital asset pricing model (CAPM). (3 points)

iii. Add the mid-point of 3-5% bond-yield premium to the long-term bond yield
obtained from Part 1. (3 points)

(4) Using the average of the three measures of the common stock cost of capital from
Part 3 as the cost of common stock, calculate the weighted average cost of capital
(WACC). (4 points)

(5) Calculate the internal rate of return (IRR) and the net present value (NPV) of the
project as follows: (4 points)
i. IRR:

ii. NPV:

(6) Decide whether to accept or reject the project. (2 points)

Answer 1

# TRUE OR FALSE

Fact	true (T) or false (F)	Reason
1. For the dividend discount model (DDM) under supernormal growth (or non-constant growth model), the discount rate (r) during the initial supernormal growth period is as same as the discount rate (r) used in the later, steady growth period.	FALSE	Because under DDM dividends will be discounted by (Ke-g), where g or growth rate will differ.
2. For the corporate valuation model (or free cash flow (FCF) discount model) in firm valuation, the cost of common equity (rc) is generally used as a discount rate.	FALSE	For corporate valuation model Ko or over all capital cost is used as discount rate
If the expected return of a stock based on the current stock price (P0) is located above the security market line (SML), then a stock analyst would issue a coverage report with a “buy” recommendation.	TRUE	if expected return is located above the SML line it means the stock is underpriced and will tend to increase. hence there will a buy recommendation
4. If the internal rate return (IRR) and the net present value (NPV) methods give conflicting results between mutually exclusive projects, the project with a higher NPV should be chosen	FALSE	Project with higher IRR should be taken because IRR shows the actual retun of a project.

# CHOOSING CORRECT STATEMENT-

1 The dividend discount model under steady growth is a suitable model for a newly- listed technology firm expected to undergo a stable growth phase in 5 to 10 years.	INCORRECT
2 For a stock with a 12% required return, if the dividend payout is expected to grow steadily at 5% (g=5%), the expected dividend yield in the following year is also 5%.	INCORRECT
3 Even when a negative dividend growth is expected, a constant-growth dividend discount model (P0 =D1/(rs−g)) can be used.	CORRECT
4 The intrinsic value of a stock is the total discounted value of all future expected dividend payouts using the dividend growth rate (g) as the discount rate.	INCORRECT
5 For a firm with zero expected growth of dividend, the dividend discount model under constant growth cannot be used.	INCORRECT

#Choose a wrong statement regarding capital budgeting

1 For a business project with a negative net present value (NPV), its internal rate of return (IRR) must be lower than the weighted average cost of capital (WACC) used to evaluate the project.	Correct
2 Because the NPV and IRR of mutually exclusive projects can give opposite results, entirely depending on the IRR method to choose a business project can minimize the risk of misjudgment.	Correct
3 The big difference between the NPV and IRR methods lies on the assumption regarding the reinvestment of cash flows during the investment periods.	Correct
4 The IRR and NPV methods always give the same results for independent projects.	Wrong

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(1) Calculate the required return to SUNNY Inc.’s stock given that the risk-free rate
is at 5%, the market risk premium is at 3% (or the expected market return at 8%),
and the beta of SUNNY, Inc. is at 1.2.

Answer- Under CAPM , Ke= Rf+ B( ERm-Rf)

Where Ke= required rate of return

Rf= Risk free rate =5%

ERm= Expected return on market

B= Beta

hence Ke of Sunny Inc stock = 5% + 1.2(8%-5%) =8.6%

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(2) SUNNY, Inc., paid a $10/share dividend in the last fiscal period and its net profits
are expected to grow at 5%. How much should SUNNY, Inc.’s stock trade per
share?

Answer-

as per Gordons model =

Po= D1/ Ke-g

where D1= D0(1+g)

g= growth rate

hence Po or Sunny inc stock price = $ 10(1+0.05) / (8.6%-5%)

=> Po= $10.5/3.6% = $291.67

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Q.SUNYK, Ltd. plans to payout a $1 per share dividend at the end of this fiscal period.
The dividend is expected to constantly grow at 5% per period. SUNYK’s required
return is 10% and the company currently trades at $22 per share. Please recommend
your investors for a decision among “hold”, “buy”, or “sell” and give your reasoning.

Answer- here D1 or Expected dividend = $1

g=5%

Ke=10%

hence fair price of the share Po= D1/ ke-g

=>Po= $1/ (10%-5%)

=>Po=$20

But the current trading price is $ 22 which is more than the fair price $20. Hence the share is over valued in the market. so the share should be sold immediately as in future the share price will be traded in its fair price $20.

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Q

10. Stony Brook Corp. recently paid an annual $15 per share dividend. From the recently
approved patent, this company’s net profits will grow at 20% in the next 2 years, and
at 5% in the third year and beyond due to expiration of the patent. The required return
to this company’s shareholders is at 10%.
(1) Calculate the intrinsic value of Stony Brook’s stock per share.

Answer-

Do or recent paid dividend = $15/share

g=20% in next 2 yaer and 5% there after

Ke or required rate of return= 10%

Intrinsic value of share = PV of dividends during super normal growth + PV of share price at the end of supernormal growth

Period	growth	Cash flow	pv@10%	Pv of cash flow
1	20%	18 (15+20%)	0.909	16.362
2	20%	21.6	0.826	17.842
2	*	453.6*	0.862	374.674
			P0 or intrinsic value	$408.88

* Calculation of Share price at the end of supernormal growth (.i. 2nd year) = P2 = D2 (1+g)/ (Ke-g)

=> P2= $21.6 (1.05) / (10%-5%)

=>P2 = $22.68/5% =$453.6

(2) Calculate the dividend yield and the capital gains yield for the first year (t=0).
Round up to the first decimal point if your answer is expressed in percentage (%)
(or up to the third decimal point if written in fraction). (4 points)

Answer=

Dividend yield in first year = Next dividend/ current price (Po)

=>($15+20%) / $408.88    (refer point 1 table)

=>$18/$408.88 = 4.40%

Capital gain yield = P1-P0 / P0

Where P1 price after one year , P0 = current price

Calculation of P1 or price after 1 year

Period	growth	Cash flow	pv@10%	Pv of cash flow
2	20%	21.6	0.909	19.6344
2		453.6	0.909	412.3224
			P1 or price after 1 year	$431.96

Capital gain yield = P1-P0 / P0

=>$431.96-$408.88 / $408.88

=>5.64%

(3) Calculate the dividend yield and the capital gains yield for the third year (as at the
beginning of the third year (t=2)). Round up to the first decimal point if your
answer is expressed in percentage (%), or up to the third decimal point if written
in fraction. (4 points)

Answer-

Dividend yield at the begin of third year = Dividend for 3rd year / price at the end of second year

=>$21.6 (1.05) / $453.6 ( refer point 1 answer)

=>$22.68/$453.6

=>5%

Capital gain yield for the third year

= (price at end of third year - price at begin og third yaer or closing of 2nd year ) / price at end of 2nd year

Calculation of price at the end of third year (P3)= D4 / (Ke-g)

=>$21.6(1.05)(1.05) / (10%-5%)

=>$23.814 / 5% = $ 476.28

Hence capital gain yield for third year=

=>$476.28- $453.6 / $453.6 = 5%

(4) What is the expected stock price of this company in five years? Round up to the
second decimal point. Provide all your calculation for partial points.

ANSWER-

Price of share at the end of 5 year (P5) = D6 / (Ke-g)

D6 Or dividend at 6 the year= $21.6 (1.05)(1.05)(1.05)(1.05) = $26.25

Hence price at the end of 5 th year = $26.25/ (10%-5%) =$525