Stock Valuation and Bond Pricing

The provided assignment covers two main topics: stock valuation and bond pricing. For the stock valuation section, it involves calculating the current price of a company's stock using the dividend growth model, given the required rate of return and constant growth rate in dividends. Additionally, it includes finding the current dividend per share when the stock's capital gains yield is equal to its dividend yield. The bond pricing part requires calculating the current price of a bond with semiannual coupon payments, given the par value, annual coupon payment, half-yearly discount rate, and number of half-years.

Running Head: FINANCE FOR BUSINESS 1
Finance for Business: Solutions to Problems

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Table of Contents
Chapter 5: Introduction to Valuation: The Time Value of Money..........................................................3
Chapter 6: Discounted Cash Flow Valuation..........................................................................................4
Chapter 7: Interest Rates and Bond Valuation......................................................................................7
Chapter 8: Stock Valuation....................................................................................................................8
References...........................................................................................................................................11

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Chapter 5: Introduction to Valuation: The Time Value of Money
Question 3
Calculating Present Values [LO2]: For each of the following, compute the present
value:
Solution
In this problem, present values have to be calculated for the given four cases. For each
of the given cases, number of years, interest rate and future values are given. Present values
can be calculated by using PV function in excel. In PV function, nper = number of periods,
rate = rate per period and fv = future value are entered to calculate respective present values.
In first case, nper = 13, rate = 9% and fv = 15451 are used to obtain pv = - 5039.79. Negative
sign signifies cash outflow. Present values can be calculated in similar way for other three
cases.
Years Interest Rate Future Value ($) Present Value ($)
13 9% 15451.00 5039.79
4 7% 51557.00 39332.59
29 24% 886073.00 1730.78
40 35% 550164.00 3.37
Question 4
Calculating Interest Rates [LO3]: Solve for the unknown interest rate in each of the
following:

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Solution
In this problem, interest rate is to be calculated for the given four cases. For this
purpose, rate function is used in excel. In rate function, nper = number of periods, pv =
present value and fv = future value are entered as inputs. In first case, nper = 4 , pv = 181 and
fv = - 297 are used to calculate rate = 13.18%. Similarly, other cases can also be evaluated.
Present Value ($) Years Future Value ($) Interest Rate
181 4 297 13.18%
335 18 1080 6.72%
48000 19 185382 7.37%
40353 25 531618 10.86%
Chapter 6: Discounted Cash Flow Valuation
Question 2
Present Value and Multiple Cash Flows [LO1]: Investment X offers to pay you
$4,700 per year for eight years, whereas Investment Y offers to pay you $6,700 per year for
five years. Which of these cash flow streams has the higher present value if the discount rate
is 5 percent? If the discount rate is 15 percent?
Solution:
Investment X consist series of eight cash inflows of $4700 per year, whereas
Investment Y pays $6700 per year for five years. Present values of are calculated for each of
the years using discount rates 5 % and 15 % for both the cash inflows. Sum of these present
values is taken to calculate the present value of cash flow streams. As can been seen, when 5
% discount rate is taken, higher present value is obtained for Investment X. However, when
15 % discount rate is used higher present value is obtained for Investment Y.
a) Investment X: Present value at 5%

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Discount Rate 5%
Year Cash Inflows ($) Present Values ($)
1 4700 4476.19
2 4700 4263.04
3 4700 4060.04
4 4700 3866.70
5 4700 3682.57
6 4700 3507.21
7 4700 3340.20
8 4700 3181.15
Total PV ($) 30377.10
b) Investment Y: Present value at 5%
Discount Rate 5%
Year Cash Inflows ($) Present Values ($)
1 6700 6380.95
2 6700 6077.10
3 6700 5787.71
4 6700 5512.11
5 6700 5249.63
Total PV ($) 29007.49
c) Investment X: Present value at 15%
Discount Rate 15%
Year Cash Inflows ($) Present Values ($)
1 4700 4086.96
2 4700 3553.88
3 4700 3090.33
4 4700 2687.24
5 4700 2336.73
6 4700 2031.94
7 4700 1766.90
8 4700 1536.44
Total PV ($) 21090.41
d) Investment Y: Present value at 15%

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Discount Rate 15%
Year Cash Inflows ($) Present Values ($)
1 6700 5826.09
2 6700 5066.16
3 6700 4405.36
4 6700 3830.75
5 6700 3331.08
Total PV ($) 22459.44
Question 20
Calculating Loan Payments [LO2, 4]: You want to buy a new sports coupe for
$79,500, and the finance office at the dealership has quoted you an APR of 5.8 percent for a
60-month loan to buy the car. What will your monthly payments be? What is the effective
annual rate on this loan?
Solution:
Annual percentage rate (APR) are quoted yearly rates for loans and are expressed in
percentage terms. APR not only includes the interest cost of borrowing but also consists other
fees that are charged by the lender (Sterling, 2008). For calculating the monthly payment of,
monthly rate is calculated by dividing APR by 12. In this problem,
Cost of Sports Coupe = $79500, Number of months = 60, APR = 5.80 %
Monthly rate = APR/12 = 0.48%
Monthly payment can be calculated by using pmt function in excel. For calculating
the loan instalment, nper = 60, pv = -79500 and rate = 0.48% are used obtain pmt = 1529.58
Monthly loan payments are equal to $1529.58
Effective annual rate = (1 + APR/n)n -1
Where n=number of periods
In case of monthly payments
Effective annual rate = (1 + APR/12)12 -1= (1 + monthly rate)12 -1

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= (1+0.48%)12-1= 5.96%
So effective annual rate is equal to 5.96%
79500
60
5.80%
0.48%
1,529.58
5.96%Effective Annual Rate
Cost of Sports Coupe($)
Tenure of Loan (Months)
Annual Percentage Rate
Monthly Rate
Monthly Payment($)
Chapter 7: Interest Rates and Bond Valuation
Question 3
Valuing Bonds [LO2]: Even though most corporate bonds in the United States make
coupon payments semiannually, bonds issued elsewhere often have annual coupon payments.
Suppose a German company issues a bond with a par value of €1,000, 23 years to maturity,
and a coupon rate of 5.8 percent paid annually. If the yield to maturity is 4.7 percent, what is
the current price of the bond?
Solution
The amount that will be paid at the maturity of the bond in the form of principal is
referred to as par value. In this question,
Coupon rate of bond= 5.80 %, therefore Coupon payment = 5.80% of € 1,000.00 = €58.00,
Years to maturity= 23 years, Yield to maturity = 4.70%.
Price of bond can be calculated by using pv function in excel. For this purpose, fv = -
1000, pmt = -58, nper = 23 and rate = 4.70% are used to calculate pv = 1152.66
Current price of the bond is calculated to be € 1,152.66

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Par Value of Bond € 1,000.00
Coupon Rate 5.80%
Coupon Payment € 58.00
Years to Maturity 23
Yield to Maturity 4.70%
Current Price of Bond € 1,152.66
Question 11
Valuing Bonds [LO2]: Union Local School District has a bond outstanding with a
coupon rate of 3.7 percent paid semiannually and 16 years to maturity. The yield to maturity
on this bond is 3.9 percent, and the bond has a par value of $5,000. What is the price of the
bond?
Solution
In this question, current price of a bond is to be calculated in case of semiannual
coupon payments. It is given that,
Par value of bond = $5000
Semiannual coupon payment = annual coupon payment/2 = (3.70%/2) x 5000 = $92.5
Half yearly discount rate = yield to maturity/2 = 3.90%/2 = 1.95%
Number of half years = years to maturity x 2 = 16 x 2 = 32
Price of bond can be calculated by using pv function in excel. For calculating pv, fv =
-5000, pmt = -92.5, nper = 32 and rate = 1.95% are used as inputs. Current price of the bond
is calculated to be $ 4881.80.
Chapter 8: Stock Valuation
Question 1
Stock Values [LO1]: The Jackson–Timberlake Wardrobe Co. just paid a dividend of
$1.95 per share on its stock. The dividends are expected to grow at a constant rate of 4
percent per year indefinitely. If investors require a return of 10.5 percent on The Jackson–

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Timberlake Wardrobe Co. stock, what is the current price? What will the price be in three
years? In 15 years?
Solution
Dividend growth rate model can be used to find price of a stock when dividends are
expected to grow at constant rate indefinitely. Expected dividend of a company, constant
dividend growth rate and required rate of are used in finding the value of a share (Corelli,
2017).
Current price of a stock = (expected dividend)/ (require rate of return – constant growth rate)
where expected dividend = current dividend x (1 + constant growth rate)
In this question, it is given that current dividend= $ 1.95, constant growth rate = 4%
and required rate of return = 10.5%
Expected dividend = 1.95 x (1 + 4%) = $2.03
Current price of stock = (2.03)/ (10.5% - 4%) = $31.20
Using dividend growth model, current price of stock is calculated to be $31.20.
Price of a stock after n years = current price x (1 + constant growth rate) n
Price of stock after 5 years = 31.20 x (1 + 4%)5 = $37.96
Price of stock after 15 years = 31.20 x (1 + 4%)15= $56.19
Current Dividend $1.95
Dividend Constant Growth Rate 4%
Expected Dividend $2.03
Required Rate of Return 10.50%
Current Stock Price $31.20
Price After 5 Years $37.96
Price After 15 Years $56.19
Question 6
Stock Valuation [LO1]: Suppose you know that a company’s stock currently sells for
$63 per share and the required return on the stock is 10.5 percent. You also know that the
total return on the stock is evenly divided between a capital gains yield and a dividend yield.

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If it’s the company’s policy to always maintain a constant growth rate in its dividends, what
is the current dividend per share?
Solution
It is known that required rate of return=dividend yield + capital gain yield
where, capital gain yield = constant dividend growth rate
In this question dividend yield = capital gain yield, therefore required rate of return=2
x constant growth rate
So, constant dividend growth rate = 10.50% / 2= 5.25%
We know that, expected dividend = current price x (required rate of return – constant
growth rate)
= 63 x (10.50 – 5.25) = $3.31
Current dividend = expected dividend/ constant growth rate= 3.31 / 5.25% = $3.14
So, current dividend is calculated to be $3.14
Current Stock Price $63.00
Required Rate of Return 10.50%
Constant Growth Rate 5.25%
Expected Dividend $3.31
Current Dividend $3.14

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References
Corelli, A. (2017). Inside company valuation. Cham, Switzerland: Springer.
Sterling, M. J. (2008). Business math for dummies. New Jersey, USA: John Wiley & Sons.