ACF 103 – Fundamentals of Finance
Tutorial 2-3 - Solutions
Chapter 3
1.
What is the total present value of the following series of cash flows,
discounted at 10%?
End of year Cash flow
1
$1,000
2
1,000
3
-2,000
4
3,000
Answer:
PV
= $1,000(PVIFA10%,2) + (-$2,000)(PVIF10%,3)+$3,000(PVIF1%,4)
= $1,000(1.736) - $2,000(0.751) + $3,000(0.683)
= $1,736 - $1,502 + $2,049 = $2,283
Actual, $2,281.95
2.
How long would it take for your money to triple if you invested it at 9%,
compounded annually?
Answer:
Let investment today equal X, then it will grow to 3X.
Thus, (X)(FVIF9%,n) = 3X or (FVIF9%,n) = 3
From Table I, FVIF9%,13 = 3.066, therefore n = a little less than 13 years.
Actual, 12.75 years
3.
At your brother's 15th birthday party, he asks you how much he would have to
deposit at the end of every month to finance a $4,250 motorcycle on his 18th
birthday. He plans to put the money in a 12% savings account that compounds
interest monthly.
Answer:
The future value interest factor of an ordinary annuity of $1 per month for 36
months (three years) at 1% per month (12% per year) is 42.077.
The table at the back of the text lists the (FVIFA1%,35) = 41.660.
This must be adjusted to 36 periods as follows: (41.660)(1.01) + 1 = 43.077.
Then $4,250/43.077 = $98.66 must be deposited at the end of each month.
4.
Text book Ch 3 question # 9 (p.66)
Answer:
Year
Amount PV Factor at 14%
1
$1,200
0.877
2
2,000
0.769
3
2,400
0.675
4
1,900
0.592
5
1,600
0.519
Subtotal (a) .................................
1–10 (annuity)*
1,400
5.216
1–5 (annuity)*
1,400
3.433
Subtotal (b) .................................
Total Present Value (a + b) .................................
ACF 103 HAUT 2014 Tutorial Solns
Present Value
$1,052.40
1,538.00
1,620.00
1,124.80
830.40
$6,165.60
$7,302.40
–4,806.20
$2,496.20
$8,661.80
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

Alternatively, to get sub-total (b):
5-10 (annuity)
1,400 (5.216 – 3.433)
2,496.20
5.
Text book Ch 3 question # 12 (p.67)
Answer:
a. Annuity of $10,000 per year for 15 years at 5%. The discount factor in the
PVIFA table at the end of the book is 10.380.
Purchase price = $10,000 × 10.380 = $103,800
b. Discount factor for 10% for 15 years is 7.606
Purchase price = $10,000 × 7.606 = $76,060
As the insurance company is able to earn more on the amount put up, it
requires a lower purchase price.
c. Annual annuity payment for 5% = $30,000/10.380 = $2,890
Annual annuity payment for 10% = $30,000/7.606 = $3,944
The higher the interest rate embodied in the yield calculations, the higher the
annual payments.
6.
Text book Ch 3 question # 13 (p.67)
Answer:
$190,000 = PMT (PVIFA17%, 20) = PMT(5.628)
PMT = $190,000/5.628 = $33,760
7.
It is January 1 and you have made a New Year's resolution to invest $2,000 in
an Individual Retirement Account (IRA) at the end of every year for the next
30 years. If your money is compounded at an average annual rate of 9%, how
much will you have accumulated at the end of 30 years?
Answer:
FVA30 = PMT(FVIFA9%,30),
FVA30 = $2,000(136.308) = $272,616
Actual, $272,615.08
8.
Congratulations! You have just won first prize in a raffle and must choose
between $20,000 in cash today or an annuity of $5,000 a year for five years.
(The annuity payments would come to you at the end of each year.) Which of
these two choices is worth more, assuming a 7% discount rate? Show your
calculations.
Answer:
PVA5 = PMT(PVIFA7%,5),
($5,000)(4.100) = $20,500
The annuity is worth more than the $20,000 in cash today.
Actual, $20,500.99
9.
Your aunt is bragging about the great investment she made in a house that she
bought 30 years ago for $20,000 and has just sold for $65,000.
a.
Calculate the rate of return on this investment.
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b.
If the average annual rate of inflation has been 3.5% during this period, was
this "a great investment?" Explain.
Answer:
a.
$65,000 = $20,000(FVIFi%,30); So, 3.25 = (FVIFi%,30),
From Table I, with n = 20, then i = a little over 4%
b.
This hardly qualifies as a "great" investment, since it has barely kept
ahead of the inflation rate.
Actual, 4.01%
10.
Ms. Early Saver has decided to invest $1,000 at the end of each year for the
next 10 years, then she will just let the amount compound for 40 additional
years. Her brother, Late Saver, has a different investment program: He will
invest nothing for the next 10 years, but will invest $1,000 per year (at the end
of each year) for the following 40 years. If we assume an 8% rate of return,
compounded annually, which investment program will be worth more 50 years
from now?
Answer:
Early Saver:
FVA10 = $1,000(FVIFA8%,10) = $1,000(14.487) = $14,487
FV40 = $14,487(FVIF8%,40) = $14,487(21.725) = $314,730.08
Late Saver: FVA40 = $1,000(FVIFA8%,40) = $1,000(259.057) = $259,057
The Early Saver investment program is worth more. (There's a moral here:
Start saving and investing as soon as you can.)
Actual, $314,713.64 versus $259,056.58
11.
Text book Ch 3 question # 1 (p.65)
Answer:
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Text book Ch 3 question # 2 (p.66)
Answer:
ACF 103 HAUT 2014 Tutorial Solns
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13.
Text book Ch 3 question # 4 (p.66)
Answer:
$50,000 = R(FVIFA8%,10) = R(14.486)
R
= $50,000/14.486
= $3,452
14.
Text book Ch 3 question # 5 (p.66)
Answer:
$50,000 = R(FVIFA8%,10)(1 + 0.08) = R(15.645)
R
= $50,000/15.645 = $3,196
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