Week 2. Chapter 4: 8, 17, and 18 and Chapter 5: 1, 4, and 12. (starting on page
ID: 2652712 • Letter: W
Question
Week 2. Chapter 4: 8, 17, and 18 and Chapter 5: 1, 4, and 12. (starting on page 120 and 155)
Ross, Stephen, Randolph Westerfield, Bradford Jordan. Essentials of Corporate Finance, 8th Edition. McGraw-Hill Learning Solutions
Calculating the Number of Periods. Solve for the unknown number of years in each of the following:
image
Calculating the Number of Periods. Calculating Rates of Return. In 2011, an 1880-O Morgan silver dollar sold for $13,113. What was the rate of return on this investment?
4.8. What is the Rate of Return? Use either the FV or the PV formula. (Show work):
r =
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Calculating Present Values. Suppose you are still committed to owning a $150,000 Ferrari (see Question 9). If you believe your mutual fund can achieve a 10.25 percent annual rate of return, and you want to buy the car in 10 years on the day you turn 30, how much must you invest today?
4.17. What must you invest today? Find the PV of a lump sum. (Show work):
PV =
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Calculating Future Values. You have just made your first $5,000 contribution to your individual retirement account. Assuming you earn a 10.1 percent rate of return and make no additional contributions, what will your account be worth when you retire in 45 years? What if you wait 10 years before contributing? (Does this suggest an investment strategy?)
4.18. What is the FV? Find the FV of a lump sum. (Show work):
a. First scenario
PV =
b. If you wait 10 years, the value of your deposit at your retirement will be:
FV =
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Present Value and Multiple Cash Flows. Rooster Co. has identified an investment project with the following cash flows. If the discount rate is 10 percent, what is the present value of these cash flows? What is the present value at 18 percent? At 24 percent?
5.1. Find the PV of each cash flow. (Show work):
a. PV@10% =
b. PV@18% =
c. PV@24% =
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Calculating Annuity Present Values. An investment offers $6,700 per year for 15 years, with the first payment occurring 1 year from now. If the required return is 8 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? For 75 years? Forever?
5.4. Find the PV of an Annuity and a Perpetuity. Hint PVA = C({1 – [1/(1 + r)^t]} / r ) (Show work):
a. PVA@15 yrs:
b. PVA@40 yrs:
c. PVA@75 yrs:
d. PV (perpetuity):
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Calculating EAR. Find the EAR in each of the following cases:
5.12 Find the EAR (Show work):
a. EAR @10%=
b. EAR @17% =
c. EAR @13% =
d. EAR @9% =
Explanation / Answer
4.8: Calculating the Number of Periods :
To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:
To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 + r)t
Solving for t, we get:
t = ln(FV / PV) / ln(1 + r)
0 t
------------------------------------------------------
-$195 $1,105
FV = $1,105 = $195 (1.09)t
t = ln($1,105 / $195) / ln 1.09
t = 20.13 years
0 t
------------------------------------------------------
-$2,105 $3,705
FV = $3,700 = $2,105(1.07)t
t = ln($3,700 / $2,105) / ln 1.07
t = 8.34 years
0 t
------------------------------------------------------
-$47,800 $387,120
FV = $387,120 = $47,800(1.12)t
t = ln($387,120 / $47,800) / ln 1.12
t = 18.46 years
0 t
------------------------------------------------------
-$38,650 $198,212
FV = $198,212 = $38,650(1.19)t
t = ln($198,212 / $38,650) / ln 1.19
t = 9.40 years
Calculating the Number of Periods. Calculating Rates of Return. In 2011, an 1880-O Morgan silver dollar sold for $13,113. What was the rate of return on this investment?
Answer:
0 131
------------------------------------------------------------
-$1 $13,113
To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 + r)t
Solving for r, we get:
r = (FV / PV)1 / t – 1
r = ($13,113 / $1)1/131 – 1
r = .0751, or 7.51%
0 t
------------------------------------------------------
-$35,000 $150,000
To answer this question, we can use either the FV or the PV formula. Both will give the same answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 + r)t
Solving for t, we get:
t = ln(FV / PV) / ln(1 + r)
FV = $150,000 = $35,000(1.032)t
t = ln($150,000 / $35,000) / ln 1.032
t = 46.20 years
4.17:
If you retire in 45 years, the value of your deposit at retirement will be:
FV=PV(1+r)^t
FV=$5000(1.105)^45
FV=$446963.97
Solution 2
If you wait 10 years before contributing, the value of your deposit at retirement will be:
FV=$5000(1.105)^35
FV=$164683.37
4.18
To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a lump sum, we use:
PV = FV / (1 + r)t
PV@10% = $830 / 1.10 + $610 / 1.102 + $1,140 / 1.103 + $1,390 / 1.104 = $3,064.57
PV@18% = $830 / 1.18 + $610 / 1.182 + $1,140 / 1.183 + $1,390 / 1.184 = $2,552.27
PV@24% = $830 / 1.24 + $610 / 1.242 + $1,140 / 1.243 + $1,390 / 1.244 = $2,251.93
5.1
To find the PVA, we use the equation:
PVA = C({1 – [1/(1 + r)t]} / r )
PVA@15 yrs: PVA = $6,700{[1 – (1/1.08)15 ] / .08} = $57,348.51
PVA@40 yrs: PVA = $6,700{[1 – (1/1.08)40 ] / .08} = $79,894.91
PVA@75 yrs: PVA = $6,700{[1 – (1/1.08)75 ] / .08} = $83,489.26
To find the PV of a perpetuity, we use the equation:
PV = C / r
PV = $6,700 / .08
PV = $83,750.00
Notice that as the length of the annuity payments increases, the present value of the annuity approaches the present value of the perpetuity. The present value of the 75-year annuity and the present value of the perpetuity imply that the value today of all perpetuity payments beyond 75 years is only $260.74.
5.4
For discrete compounding, to find the EAR, we use the equation:
EAR = [1 + (APR / m)]m – 1
EAR = [1 + (.10 / 4)]4 – 1 = .1038, or 10.38%
EAR = [1 + (.17 / 12)]12 – 1 = .1839, or 18.39%
EAR = [1 + (.13 / 365)]365 – 1 = .1388, or 13.88%
EAR = [1 + (.09 / 2)]2 – 1 = .0920, or 9.20%
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