a. Anna is presented with the following stream of cash flows from an investment
ID: 2465329 • Letter: A
Question
a. Anna is presented with the following stream of cash flows from an investment over the next 5 years: End of year Cash flow ($) 1 $500 2 $800 3 $500 4 $400 5 $300 If the relevant rate of interest is 8.5% per annum on this investment, how much should Anna pay for this investment opportunity? If the same investment product is for sale for $3,000 today, should Anna purchase the investment?
b. Western Financing Group offers a loan of $200,000 with an interest rate of 8.5% per annum. The loan is to be paid off by 20 equal quarterly payments; the first payment is due today (at the time of the loan approval). Find the size of the quarterly payment.
Explanation / Answer
a.
Anna should pay at most the present value of the cash flows from the investment.
Year
Cash flow
Present value factor @ 8.5%
Present value of cash flow
1
$500.00
0.9217
$460.85
2
$800.00
0.8495
$679.60
3
$500.00
0.7829
$391.45
4
$400.00
0.7216
$288.64
5
$300.00
0.6651
$199.53
$2,020.07
Hence, Anna should pay not more than @$2,020.07 for this investment opportunity.
If the same investment product is for sale for $3,000 today, Anna should not purchase the investment because the fair value of the investment i.e. $2,020.07 is less than $3,000.
b.
Annual interest rate = 8.5%
Quarterly interest rate = 8.5% / 4 = 2.125% = 0.02125
No. of payments = 20
Loan value = $200,000
Let the quarterly payment be X.
Loan amount to be repaid from year 1 = $200,000 – X
No. of payments from year 1 = 20 – 1 = 19
Loan payment = (Loan value * Interest rate) / {1 – (1+interest rate)-No. of payments}
X = {($200,000 – X) * 0.02125} / ( 1 – 1.02125-19)
X = ($4,250 – 0.02125*X) / 0.3294
0.3294*X + 0.02125*X = $4,250
0.35065 * X = $4,250
X = $4,250 / 0.35065 = $12,120.35
Hence, size of quarterly payment = $12,120.35
Year
Cash flow
Present value factor @ 8.5%
Present value of cash flow
1
$500.00
0.9217
$460.85
2
$800.00
0.8495
$679.60
3
$500.00
0.7829
$391.45
4
$400.00
0.7216
$288.64
5
$300.00
0.6651
$199.53
$2,020.07
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