Question

Part A Your sister is celebrating her 30th birthday. As the party winds down she asks you for some help. She wants to start saving for her retirement at age 60. She tells you that ideally she would like to withdraw $50,000 on an annual basis for 20 years starting the year after she retires. She says that she would be comfortable putting aside some money each year in an annuity and believes that she would be able to earn an 8% rate of return. If your sister starts making annuity payments to her savings accounts at the end of this year and makes her last deposit at age 60, how much must she deposit each year? (5 marks) Your sister mentions that she currently has a savings account of $25,000 if she used that money to start the account, how much must she deposit each year until she reaches age 60 ii. (5 marks) She suddenly remembers that as children your parents bought both you and her a life insurance policy that matures on her 50th birthday for an amount of $50,000. If she added that to the retirement fund, along with her $25,000 (year 0) savings account, how much must she deposit each year until she reaches (5 marks) age 60? Part B State Street has bonds outstanding with a $1,000 face value and 10 years left to maturity. They have an 11% annual coupon payment and their current price is $1,175 The bonds may be called in 5 years at 9% premium. Jay has managed to save some money after working for 5 years and wants to invest in the bond market. Jay is considering to buy State Street's bond whose rating is now rated by S&P as ABB. Required What is the bond's yield to maturity? What is the bond's yield to call? ii. (3 marks) (3 marks If Jay were to buy this bond, would he be more likely to receive the yield to maturity or the yield to call? Explain your answer. (4 marks)

Answer 1

Part-A

(i)	Present value at 30th year of 20 years cashflows after 30 years :							Computation of Deposits for 30 years :
	Year	CF	PV (@8%)				year of Deposit	Compounded for Years	CF	FV Factor (8%)	FV
1	31	50000	46296.3				1	29	4372.05	9.32	40735.55
2	32	50000	42866.94				2	28	4372.05	8.63	37718.11
3	33	50000	39691.61				3	27	4372.05	7.99	34924.17
4	34	50000	36751.49				4	26	4372.05	7.40	32337.20
5	35	50000	34029.16				5	25	4372.05	6.85	29941.85
6	36	50000	31508.48				6	24	4372.05	6.34	27723.93
7	37	50000	29174.52				7	23	4372.05	5.87	25670.31
8	38	50000	27013.44				8	22	4372.05	5.44	23768.81
9	39	50000	25012.45				9	21	4372.05	5.03	22008.15
10	40	50000	23159.67				10	20	4372.05	4.66	20377.92
11	41	50000	21444.14				11	19	4372.05	4.32	18868.44
12	42	50000	19855.69				12	18	4372.05	4.00	17470.78
13	43	50000	18384.9				13	17	4372.05	3.70	16176.65
14	44	50000	17023.05				14	16	4372.05	3.43	14978.38
15	45	50000	15762.09				15	15	4372.05	3.17	13868.87
16	46	50000	14594.52				16	14	4372.05	2.94	12841.55
17	47	50000	13513.45				17	13	4372.05	2.72	11890.32
18	48	50000	12512.45				18	12	4372.05	2.52	11009.56
19	49	50000	11585.6				19	11	4372.05	2.33	10194.03
20	50	50000	10727.41				20	10	4372.05	2.16	9438.92
							21	9	4372.05	2.00	8739.74
		Total	490907.4				22	8	4372.05	1.85	8092.35
							23	7	4372.05	1.71	7492.92
							24	6	4372.05	1.59	6937.89
							25	5	4372.05	1.47	6423.97
							26	4	4372.05	1.36	5948.12
							27	3	4372.05	1.26	5507.52
							28	2	4372.05	1.17	5099.55
							29	1	4372.05	1.08	4721.81
									Aggregate FV Factor for 30 years	112.28	490907.37
									Deposits each year	(490907.4)/112.28	4372.05

(ii)
year of Deposit	Compounded for Years	CF	FV Factor (8%)	FV
0	30	25000	10.06	251566.42
1	29	2131.58	9.32	19860.54
2	28	2131.58	8.63	18389.39
3	27	2131.58	7.99	17027.21
4	26	2131.58	7.40	15765.94
5	25	2131.58	6.85	14598.09
6	24	2131.58	6.34	13516.75
7	23	2131.58	5.87	12515.51
8	22	2131.58	5.44	11588.44
9	21	2131.58	5.03	10730.03
10	20	2131.58	4.66	9935.22
11	19	2131.58	4.32	9199.27
12	18	2131.58	4.00	8517.85
13	17	2131.58	3.70	7886.89
14	16	2131.58	3.43	7302.68
15	15	2131.58	3.17	6761.74
16	14	2131.58	2.94	6260.87
17	13	2131.58	2.72	5797.10
18	12	2131.58	2.52	5367.69
19	11	2131.58	2.33	4970.08
20	10	2131.58	2.16	4601.93
21	9	2131.58	2.00	4261.04
22	8	2131.58	1.85	3945.41
23	7	2131.58	1.71	3653.16
24	6	2131.58	1.59	3382.55
25	5	2131.58	1.47	3131.99
26	4	2131.58	1.36	2899.99
27	3	2131.58	1.26	2685.18
28	2	2131.58	1.17	2486.28
29	1	2131.58	1.08	2302.11
		Aggregate FV Factor for 30 years	112.28	490907.37
		Deposits each year	(490907.4-251566.42)/112.28	2131.58

(iii)
year of Deposit	Compounded for Years	CF	FV Factor (8%)	FV
0	30	25000	10.06	251566.42
1	29	1170.21	9.32	10903.15
2	28	1170.21	8.63	10095.51
3	27	1170.21	7.99	9347.69
4	26	1170.21	7.40	8655.27
5	25	1170.21	6.85	8014.14
6	24	1170.21	6.34	7420.50
7	23	1170.21	5.87	6870.83
8	22	1170.21	5.44	6361.88
9	21	1170.21	5.03	5890.63
10	20	1170.21	4.66	5454.29
11	19	1170.21	4.32	5050.27
12	18	1170.21	4.00	4676.17
13	17	1170.21	3.70	4329.79
14	16	1170.21	3.43	4009.07
15	15	1170.21	3.17	3712.10
16	14	1170.21	2.94	3437.13
17	13	1170.21	2.72	3182.53
18	12	1170.21	2.52	2946.78
19	11	1170.21	2.33	2728.50
20	10	50000.00	2.16	107946.25
20	10	1170.21	2.16	2526.39
21	9	1170.21	2.00	2339.25
22	8	1170.21	1.85	2165.97
23	7	1170.21	1.71	2005.53
24	6	1170.21	1.59	1856.97
25	5	1170.21	1.47	1719.42
26	4	1170.21	1.36	1592.05
27	3	1170.21	1.26	1474.12
28	2	1170.21	1.17	1364.93
29	1	1170.21	1.08	1263.82
		Aggregate FV Factor for 30 years	112.28	490907.37
		Deposits each year	(490907.4-251566.42-107946.25)/112.28	1170.21

Part - B