Question 1

If D1 = $1.25, g (which is constant) = 5.5%, and P0 = $44, what is the stock's expected total return for the coming year?

Accepted Answer

$\begin{array}{lr}
\mathrm{D}_{1} & \$ 1.25 \
\mathrm{~g} & 5.5 \% \
\mathrm{P}_{0} & \$ 44.00 \
\text { Total return }=r_{\mathrm{S}}=\mathrm{D}_{1} / \mathrm{P}_{0}+\mathrm{g} & 8.34 \%
\end{array}$

Question 2

A stock just paid a dividend of D0 = $1.50. The required rate of return is rs = 10.1%, and the constant growth rate is g = 4.0%. What is the current stock price?

Accepted Answer

$\begin{array}{lr}
\mathrm{D}_{0} & \$ 1.50 \
\mathrm{r}_{\mathrm{s}} & 10.1 \% \
\mathrm{~g} & 4.0 \% \
\mathrm{D}_{1}=\mathrm{D}_{0}(1+\mathrm{g})= & \$ 1.56 \
\mathrm{P}_{0}=\mathrm{D}_{1} /\left(\mathrm{r}_{\mathrm{S}}-\mathrm{g}\right) & \$ 25.57
\end{array}$

Question 3

A new investment opportunity for you is an annuity that pays $550 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Accepted Answer

BEGIN Mode
 $\begin{array}{lr}
\text { N } & 3 \
\text { I/YR } & 5.5 \% \
\text { PMT } & \$ 550 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 1,565.48
\end{array}$

Question 4

If D0 = $2.25, g (which is constant) = 3.5%, and P0 = $50, what is the stock's expected dividend yield for the coming year?

Accepted Answer

$\begin{array}{lr}
\mathrm{D}_{0} & \$ 2.25 \
\mathrm{~g} & 3.5 \% \
\mathrm{P}_{0} & \$ 50.00 \
\mathrm{D}_{1}=\mathrm{D}_{0}(1+\mathrm{g})= & \$ 2.329 \
\text { Dividend yield }=\mathrm{D}_{1} / \mathrm{P}_{0}= & 4.66 \%
\end{array}$

Question 5

Because your mother is about to retire, she wants to buy an annuity that will provide her with $75,000 of income a year for 20 years, with the first payment coming immediately. The going rate on such annuities is 5.25%. How much would it cost her to buy the annuity today?

Accepted Answer

BEGIN Mode
 $\begin{array}{lr}
\text { N } & 20 \
\text { I/YR } & 5.25 \% \
\text { PMT } & \$ 75,000 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 963,213
\end{array}$

Question 6

If D0 = $1.75, g (which is constant) = 3.6%, and P0 = $32.00, what is the stock's expected total return for the coming year?

Accepted Answer

$\begin{array}{lccc}
\mathrm { D } _ { 0 } & \$ 1.75 \
\mathrm {~B} & 3.6 \% \
\mathrm { P } _ { 0 } & \$ 32.00 \
\mathrm { D } _ { 1 } = \mathrm { D } _ { 0 } ( 1 + \mathrm { g } ) = & \$ 1.81 \
\text { Total retur1 } = r _ { s } = \mathrm { D } _ { 1 } / \mathrm { P } _ { 0 } + \mathrm { g } & \mathbf { 9 . 2 7 \% }
\end{array}$

Question 7

A share of Lash Inc.'s common stock just paid a dividend of $1.00. If the expected long-run growth rate for this stock is 5.4%, and if investors' required rate of return is 11.4%, what is the stock price?

Accepted Answer

$\begin{array}{lr}
\text { Last dividend }\left(\mathrm{D}_{0}\right) & \$ 1.00 \
\text { Long-run growth rate } & 5.4 \% \
\text { Required return } & 11.4 \% \
\mathrm{D}_{1}=\mathrm{D}_{0}(1+\mathrm{g})= & \$ 1.054 \
\mathrm{P}_{0}=\mathrm{D}_{1} /\left(\mathrm{r}_{\mathrm{S}}-\mathrm{g}\right) & \$ 17.57
\end{array}$

Question 8

If D1 = $1.25, g (which is constant) = 4.7%, and P0 = $26.00, what is the stock's expected dividend yield for the coming year?

Accepted Answer

$\begin{array}{lr}
\mathrm{D}_{1} & \$ 1.25 \
\mathrm{~g} & 4.7 \% \
\mathrm{P}_{0} & \$ 26.00 \
\text { Dividend yield }=\mathrm{D}_{1} / \mathrm{P}_{0}= & 4.81 \%
\end{array}$

Question 9

Kelly Enterprises' stock currently sells for $35.25 per share. The dividend is projected to increase at a constant rate of 4.75% per year. The required rate of return on the stock, rs, is 11.50%. What is the stock's expected price 5 years from now?

Accepted Answer

$\begin{array}{lr}
\text { Growth rate } & 4.75 \% \
\text { Years in the future } &5 \
\text { Stock price } & \$ 35.25  \
P_{5}=P_{0}(1+g)^{5}= & \$ 44.46
\end{array}$

Question 10

What annual payment must you receive in order to earn a 6.5% rate of return on a perpetuity that has a cost of $1,250?

Accepted Answer

$\begin{array}{ll}
\text { Cost }(\mathrm{PV}) & \$ 1,250 \
\text { UYR } & 6.5 \% \
\text { PMT } & \$ 81.25 \text { Multiply Cost by I/YR }
\end{array}$

Question 11

A salt mine you inherited will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the mine is 7.5%, how much should you ask for it if you decide to sell it?

Accepted Answer

BEGIN Mode
 $\begin{array}{lr}
\text { N } & 25 \
\text { I/YR } & 7.5 \% \
\text { PMT } & \$ 25,000 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 299,574
\end{array}$

Question 12

Franklin Corporation is expected to pay a dividend of $1.25 per share at the end of the year (D1 = $1.25). The stock sells for $32.50 per share, and its required rate of return is 10.5%. The dividend is expected to grow at some constant rate, g, forever. What is the equilibrium expected growth rate?

Accepted Answer

$\begin{array}{lr}
\text { Expected dividend }\left(\mathrm{D}_{1}\right) & \$ 1.25 \
\text { Stock price } & \$ 32.50 \
\text { Required return } & 10.5 \% \
\text { Dividend yield } & 3.85 \% \
\text { Growth rate }=r_{\mathrm{S}}-\mathrm{D}_{1} / \mathrm{P}_{0}= & 6.65 \%
\end{array}$

Question 13

You were left $100,000 in a trust fund set up by your grandfather. The fund pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?

Accepted Answer

BEGIN Mode
 $\begin{array}{lr}
\text { N } & 4 \
\text { I/YR } & 6.5 \% \
\text { PV } & \$ 100,000 \
\text { FV } & \$ 0.00 \
\text { PMT } & \$ 27,409
\end{array}$

Question 14

If D1 = $1.50, g (which is constant) = 6.5%, and P0 = $56, what is the stock's expected capital gains yield for the coming year?

Accepted Answer

$\begin{array}{lr}
\mathrm{D}_{1} & \$ 1.50 \
\mathrm{~g} & 6.5 \% \
\mathrm{P}_{0} & \$ 56.00 \
\text { Capital gains yield }=\mathrm{g}= & 6.50 \%
\end{array}$

Question 15

Geraldine was injured in a car accident, and the insurance company has offered her the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave her as well off financially as with the annuity?

Accepted Answer

BEGIN Mode
 $\begin{array}{lr}
\text { N } & 15 \
\text { I/YR } & 7.5 \% \
\text { PMT } & \$ 25,000 \
\text { FV } & \$ 0.00 \
\text { PV } & \$ 237,229
\end{array}$

Question 16

Your aunt wants to retire and has $375,000. She expects to live for another 25 years and to earn 7.5% on her invested funds. How much could she withdraw at the end of each of the next 25 years and end up with zero in the account?

Accepted Answer

$\begin{array}{ll}
\text { N } & 25 \
\text { I/YR } & 7.5 \% \
\text { PV } & \$ 375,000 \
\text { FV } & \$ 0.00 \
\text { PMT } & \$ 33,641.50
\end{array}$

Question 17

What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?

Accepted Answer

$\begin{array}{lr}
\text {N} & 4 \
\text { I/YR } & 5.0 \% \
\text { PMT } & \$ 2,250 \
\text { FV } & \$ 3,000 \
\text { PV } & \$ 10,446
\end{array}$ 
Alternative setup:
 $\begin{array}{ccccc}
\hline 0& 1 & 2 & 3 & 4 \
\hline & \$ 2,250 & \$ 2,250 & \$ 2,250 & \$ 2,250 \
& & & & \$ 3,000 \
\hline & \$ 2,250 & \$ 2,250 & \$ 2,250 & \$ 5,250 \
\hline P V=\$ 10,446.50 & & & &
\end{array}$

Question 18

$35.50 per share is the current price for Foster Farms' stock. The dividend is projected to increase at a constant rate of 5.50% per year. The required rate of return on the stock, rs, is 9.00%. What is the stock's expected price 3 years from today?

Accepted Answer

$\begin{array}{l}
\begin{array} { l } 
\text { Stock price } \
\text { Growth rate } \
\text { Years in the future } \
P _ { 3 } = P _ { 0 } ( 1 + g ) ^ { 3 } =
\end{array}
\begin{array} { l } 
\$ 35.50 \
5.50 \% \
3 \
\$ 41.69
\end{array}
\end{array}$

Question 19

Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to open a new restaurant, and your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?

Accepted Answer

BEGIN Mode
 $\begin{array}{ll}
\text { N } & 12 \
\text { PV } & \$ 120,000 \
\text { PMT } & \$ 15,000 \
\text { FV } & \$ 0.00 \
\text { I/YR } & 841 \%
\end{array}$

Question 20

Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.

Accepted Answer

$\begin{array}{ll}
N & 20 \
\mathrm{PV} & \$ 2,550,000 \
\mathrm{PMT} & \$ 250,000 \
\mathrm{FV} & \$ 0.00 \
\mathrm{I} / \mathrm{YR} & 749 \%
\end{array}$

Quiz 29: Basic Financial Tools: A review