5. Nominal versus Real Returns: a. In nominal terms? b. In real terms? The nominal return is 10.23% from the table. To find the real return, we use the fisher equation (1 + R) = (1 + r) (1 + h)...

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5. Nominal versus Real Returns:



a. In nominal terms?


b. In real terms?



  1. The nominal return is 10.23% from the table.



  1. To find the real return, we use the fisher equation



(1 + R) = (1 + r) (1 + h)
(1 + 0.1023) = (1 + r) (1 + 0.0406)
1.1023 = (1 + r) (1.0406)
1 + r = 1.0593
r = 1.0593 – 1
r = 0.0593 or 5.93%

7. Calculating Returns and Variability:



Returns


Year X Y



1 6% 18%



2 24 39



3 13 -6



4 -14 -20



5 15 47

Return X
Arithmetic average returns, R = [R1
+R2
+ R3
+ R4
+ R5]/N
= [0.06 + 0.24 + 0.13 - 0.14 + 0.15]/5
= 0.44/5
= 0.088 or 8.80%
Variance = 1/ (N – 1) [(R1
– R)
2
+ (R2
– R)
2
+ (R3
– R)
2
+ (R4
– R)
2+ (R5
– R)
2]
= 1/ (5 – 1) [(0.06 – 0.088)2
+ (0.24 – 0.088)2
+ (0.13 – 0.088)2
+ (-0.14 – 0.088)2+ (0.15 – 0.088)2]
= ¼ [0.08148]
= 0.02037
Standard deviation = vVariance
= v0.02037
= 0.1427 or 14.27%
Return Y

Arithmetic average returns, R = [R1
+R2
+ R3
+ R4
+ R5]/N
= [0.18 + 0.39 + (-0.06) + (-0.20) + 0.47]/5
= 0.78/5
= 0.1560 or 15.60%
Variance = 1/ (N – 1) [(R1
– R)
2
+ (R2
– R)
2
+ (R3
– R)
2
+ (R4
– R)
2+ (R5
– R)
2]
= 1/ (5 – 1) [(0.18 – 0.156)2
+ (0.39 – 0.156)2
+ (-0.06 – 0.156)2
+ (-0.20 – 0.156)2+ (0.47 – 0.156)2]
= ¼ [0.32732]
= 0.08183
Standard deviation = vVariance
= v0.08183
= 0.2861 or 28.61%

8. Risk Premiums:


a. Calculate the arithmetic average returns for large-company stocks and T-Bills over this period.


b. Calculate the standard deviation of the returns for large-company stocks and T-Bills over this period.


c. Calculate the observed risk premium in each year for the large-company stocks versus T-Bills. What was the average risk premium over this period? What was the standard deviation of the risk premium over this period?


d. Is it possible for the risk premium to be negative before an investment is undertaken? Can the risk premium be negative after the fact?





















































YearLarge stock returnT-bill returnRisk premium
1970-3.57%6.89-10.46
19718.013.864.15
197227.373.4323.94
19730.274.78-4.51
1974-25.937.68-33.61
197518.487.0511.43
Total24.6333.69-9.06


  1. Large Company Stocks



Arithmetic average returns, R = [R1
+R2
+ R3
+ R4
+ R5
+ R6]/N
= 24.63/6
= 4.105%
T-bills
Arithmetic average returns, R = [R1
+R2
+ R3
+ R4
+ R5
+ R6]/N
= 33.69/6
= 5.615%


  1. Large Company Stocks



Variance = 1/ (N – 1) [(R1
– R)
2
+ (R2
– R)
2
+ (R3
– R)
2
+ (R4
– R)
2+ (R5
– R)
2
+ (R6
– R)
2]
= 1/ (6 – 1) [(-3.57 – 4.105)2
+ (8.01 – 4.105)2
+ (27.37 – 4.105)2
+ (0.27 – 4.105)2+ (-25.93 – 4.105)2+ (18.48 – 4.105)2]
= 1/5 [0.173885]
= 0.034777
Standard deviation = vVariance
= v0.034777
= 0.1865 or 18.65%
T-bills
Variance = 1/ (N – 1) [(R1
– R)
2
+ (R2
– R)
2
+ (R3
– R)
2
+ (R4
– R)
2+ (R5
– R)
2
+ (R6
– R)
2]
= 1/ (6 – 1) [(6.89 – 5.615)2
+ (3.86 – 5.615)2
+ (3.43 – 5.615)2
+ (4.78 – 5.615)2+ (7.68 – 5.615)2+ (7.05 – 5.615)2]
= 1/5 [0.00165005]
= 0.00033001
Standard deviation = vVariance
= v0.00033001
= 0.0182 or 1.82%


  1. Average observed risk premium = [R1
    +R2
    + R3
    + R4
    + R5
    + R6]/N = -9.06/6 = -1.51%



Variance = 1/ (N – 1) [(R1
– R)
2
+ (R2
– R)
2
+ (R3
– R)
2
+ (R4
– R)
2+ (R5
– R)
2
+ (R6
– R)
2]
= 1/ (6 – 1) [(-10.46 – 1.51)2
+ (4.15 – 1.51)2
+ (23.94 – 1.51)2
+ (-4.51 – 1.51)2+ (-33.61 – 1.51)2+ (11.43 – 1.51)2]
= 1/5 [0.1966694]
= 0.03933
Standard deviation = vVariance
= v0.03933
= 0.1983 or 19.83%
d) Before the fact, the risk premium will positive, investors demand compensation above the risk-free return to invest money. After the fact, the risk premium can be negative if assets nominal return is low and risk-free return is high unexpectedly.

9. Calculating Returns and Variability:


a. What was the arithmetic average return on Crash-n-Burn’s stock over this 5-year period?


b. What was the variance of Crash-n-Burn’s returns for this period? The standard deviation?



  1. Arithmetic average return, R = [R1
    +R2
    + R3
    + R4
    + R5]/N



= [0.02 + (-0.08) + 0.24 + 0.19 + 0.12]/5
= 0.49/5
= 0.098 or 9.80%


  1. Variance = 1/(N – 1) [(R1
    – R)2
    + (R2
    – R)2
    + (R3
    – R)2
    + (R4
    – R)2+ (R5
    – R)2]



= 1/ (5 – 1) [(0.02 – 0.098)2
+ (-0.08 – 0.098)2
+ (0.24 – 0.098)2
+ (0.19 – 0.098)2+ (0.12 – 0.098)2]
= ¼ [0.06688]
= 0.01672
Standard deviation = vVariance
= v0.01672
= 0.1293 or 12.93%

12. Effects of Inflation:


T-bill rates were highest in initial period. During the period of high inflation, it was consistent in accordance with the Fisher effect.

13. Calculating Investment Returns:


Given that Coupon rate = 7%,
Price 1 year ago, P1 = $920
Required return on bond, I = 8%
Number of years, n = 6
Inflation rate, h = 4.2%
To find total real return, we have to find the nominal return based on the current price of bond. Now,
Coupon payment, C = 0.07 x 1000 = $70
P1 = C (PVIFA @ 8%, 6) + Face value (PVIF @ 8%, 6)
= $70 [(1.086
– 1)/ (0.08*1.086)] + 1000/1.086

= $70 (0.58687/0.12695) + 630.17
= $70 (4.6228) + 630.17
= $323.60 + $630.17
= $953.77
Nominal return, R = [(P1 – P0 + C]/P0
= [(953.77 – 920 + 70]/920
= 103.77/920
= 0.1128 or 11.28%
Using the fisher equation,
(1 + R) = (1 + r) (1 + h)
(1 + 0.1128) = (1 + r) (1 + 0.042)
(1.1128) = (1 + r) (1.042)
1 + r = 1.1128/1.042
1 + r = 1.0679
r = 1.0679 – 1
r = 0.0679 or 6.79%
The total real return on investment is 6.79%
005_b4usajo-orr5ramp.doc
Answered Same DayDec 22, 2021

Answer To: 5. Nominal versus Real Returns: a. In nominal terms? b. In real terms? The nominal return is 10.23%...

Robert answered on Dec 22 2021
124 Votes
Business Finance (FIN2304)
Final Exam “A”
Page 16 of 16
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Short Answer #1 /5
Short Answer #2 /5
Short Answer #3 /5
Short Answer #4 /5
Short Answer #5 /5
Short Answer #5 /5
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Long Answer #2 /15
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This Exam consists of 25 Multiple Choice questions - 50 marks, 6 Short Problem questions - 30 marks, 3 Long Problem questions - 45 marks, for a Total of 125 marks.
PART A – Multiple Choice (2 marks each, total 50 marks)
Use the following to answer questions 1-3:
Use the following to answer the question(s) below. A savings account, which started with a balance of $500, has the following end of year balances. No withdrawals were made over the life of the account, but there was one additional deposit of $50 made at the beginning of year 5.
Year 1 = $550; Year 2 = $580; Year 3 = $660; Year 4 = $772; Year 5 = $950
1.
If you leave the money in the account for another five years and the account earns 8% compounded annually, what will the balance in the account grow to?
A)
$1,341.05
B)
$1,347.82
C)
$1,395.86
D)
$1,406.23
E)
$1,491.15
2.
Over the first four years, the account earned ________ compounded annually.
A)
11.5%
B)
12.8%
C)
14.6%
D)
15.6%
E)
23.1%
3.
If the account earned a total of $300 in simple interest over its life, how much was earned in compound interest?
A)
$25
B)
$50
C)
$75
D)
$100
E)
$125
4.
You received a $1 savings account earning 5% on your 1st birthday. How much will you have in the account on your 40th birthday if you don't withdraw any money before then?
A)
$5.89
B)
$6.34
C)
$6.70
D)
$7.00
E)
$7.04
5.
You borrowed $1,500 at 6% compounded annually. Your payments are $90 at the end of each year. How many years will you make payments on the loan?
A)
9 years
B)
10 years
C)
11 years
D)
12 years
E)
forever
6.
The amount by which the call price exceeds the bond's par value is the:
A)
Coupon rate
B)
Redemption value.
C)
Call premium
D)
Original-issue discount
E)
Call rate
7.
Assume the required return on a zero-coupon bond will remain constant over the remainder of its life. The market value of the bond will:
A)
Increase each year by an amount equal to the imputed coupon rate for the period
B)
Increase each year by an amount equal to the imputed interest for the period
C)
Decrease each year by an amount equal to the imputed interest for the period
D)
Decrease each year by an amount equal to the bond's yield to maturity
E)
Remain unchanged
8.
If investors are uncertain that they will be able to sell a corporate bond quickly, the investors will demand a higher yield in the form of a(n) _________________.
A)
inflation premium
B)
interest rate risk premium
C)
default risk premium
D)
liquidity risk premium
E)
increased real rate of interest
9.
________________ is an account into which periodic payments are made for the purpose of retiring a bond issue.
A)
An indenture
B)
A debenture
C)
A covenant
D)
A call option
E)
A sinking fund
10.
Which of the following terms is typically associated with BOTH preferred stock and common stock?
A)
Proxy
B)
Voting rights
C)
Dividend yield
D)
Arrearage
E)
Cumulative voting
11.
Saskatchewan Steel, Ltd. and Alberta Copper, Inc. both recently announced earnings of $400,000. Both companies have common shares outstanding of 250,000 and rates of return of 10%. Saskatchewan Steel has a new project that will generate net cash flows of $50,000 per year forever. Alberta Copper has a new project that will generate net cash flows of $40,000 per year forever. The stock price of Saskatchewan Steel should be _______ greater than the stock price of Alberta Steel.
A)
$0.04
B)
$0.40
C)
$3.60
D)
$10,000
E)
$100,000
12.
The process of valuing an investment by determining the present value of its future cash flows is called (the):
A)
Constant dividend growth model
B)
Discounted cash flow valuation
C)
Average accounting valuation
D)
Expected earnings model
E)
Capital Asset Pricing Model
13.
Which capital investment evaluation technique is described by the following characteristics? (1) Easy to understand; (2) Biased towards liquidity; (3) Requires an arbitrary cutoff point; (4) Ignores the time value of money.
A)
NPV
B)
IRR
C)
Profitability index
D)
Payback period
E)
Discounted...
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