Question

Question 2

You are offered a special set of annuities by your insurance company, whereby you will receive $23,600 a year for the next 7 years, nothing for the next 10 years, and then $40,000 a year for the following 12 years. How much would you be willing to pay for these annuities today, if the annuities are paid at the beginning of each year? Assume the annuities have a beta of 1.47, the expected return on the market is 12.4% and the risk free rate is 2.4%.

	1.	$105,878
	2.	$123,983
	3.	$139,697
	4.	$158,123
	5.	$185,123

Answer 1

The correct answer is option B i.e. $123983

As per CAPM, Expected Return = Risk free Rate + Beta x (Return on market - risk free rate)

Expected Return = 2.4% + 1.47  x (12.40% -2.40%) =17.10%

Year	Annuity	PV of annuity
0	$       23,600	$             23,600
1	$       23,600	$             20,154
2	$       23,600	$             17,211
3	$       23,600	$             14,697
4	$       23,600	$             12,551
5	$       23,600	$             10,718
6	$       23,600	$                9,153
7		$                       -
8		$                       -
9		$                       -
10		$                       -
11		$                       -
12		$                       -
13		$                       -
14		$                       -
15		$                       -
16		$                       -
17	$       40,000	$                2,733
18	$       40,000	$                2,334
19	$       40,000	$                1,993
20	$       40,000	$                1,702
21	$       40,000	$                1,453
22	$       40,000	$                1,241
23	$       40,000	$                1,060
24	$       40,000	$                   905
25	$       40,000	$                   773
26	$       40,000	$                   660
27	$       40,000	$                   564
28	$       40,000	$                   481
NPV	123983

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