question archive Assume that you just won the government vaccination lottery

Assume that you just won the government vaccination lottery

Subject:AccountingPrice:9.82 Bought3

Share With

Assume that you just won the government vaccination lottery. Your prize can be taken either in the form of $100,000 at the end of each of the next 20 years (i.e., $2 million over 20 years) or as a lump sum of $1,000,000 paid immediately.

(a) If you expect to invest $100,000 annually that earns 6% annually on your investments over the next 20 years, calculate the current value of future payments from an annuity. Explain how you would use time value of money analysis to choose between the annuity and the lump sum.

(b) If you expect to invest $100,000 annually that earns 8% annually on your investments over the next 20 years, calculate the current value of future payments from an annuity. Explain how you would use time value of money analysis to choose between the annuity and the lump sum.

c) Using interpolation based on your answers in part (a) and (b), at approximately what interest rate would you be indifferent when choosing between the two plans?

(d) You can earn 3 percent, compounded monthly at your bank. If you deposit $1,000,000 at age 28, how old will you be when your account has grown to $2,000,000? What is the effective annual rate?

Question 2 Becky Kwok is currently considering investing specified amounts in the following two investment opportunities described below.

• Investment A: Invest a lump sum of $52,000 today in an account that pays 8% annual interest, compounded monthly and leave the funds on deposit for exactly 10 years.

• Investment B: Invest $1,200 at the beginning of each month for the next 5 years in an account that pays 10% annual interest, compounded monthly.

(a) For investment A, draw the necessary timeline and determine the account balance at the end of year 10.

(b) For investment B, draw the necessary timeline and determine the account balance at the end of year 5.

Question 3 Four years ago, SONO Ltd. raised $30 million by issuing 15-year $1,000 par value bonds that carry 6.8% coupon rate, payable semiannually. SONO Ltd. is currently announcing to raise another $20 million by issuing 15-year zero coupon bonds that discount semi-annually. The current YTM on these bonds is 9%.

(a) Calculate the number of the 15-year coupon bonds that SONO Ltd. issued to raise the $30 million four years ago. What will be the company's repayment be at the maturity date of the 15-year coupon bonds?

(b) Calculate the current bond prices of the 15-year coupon bonds and 15-year zero coupon bonds.

(c) Calculate the number of the 15-year zero coupon bonds that SONO Ltd. currently issues to raise the $20 million. What will be the company's repayment be at the maturity date of the 15-year zero coupon bonds?

(d) Are 15-year 6.8% coupon bonds or 15-year zero coupon bonds more sensitive to changes in market interest rates? (2 marks)

Name: Assume that you just won the government vaccination lottery. Your prize can be taken either in the f
Brand: Study Help Me
SKU: 100185
Price: 10 USD
Availability: LimitedAvailability
Rating: 5 (3 reviews)

pur-new-sol

Purchase A New Answer

Custom new solution created by our subject matter experts

GET A QUOTE

Answer Preview

given below.

Step-by-step explanation

Q1)

Present value of annuity = P*[1 - (1+r)^-n / r ]

P = Periodical payment

r = Interest rate

n = Number of periods

Present value = 100000*[1 - (1+6%)^-20 / 6% ]

= 1,146,992.12

we compare the present value with Lumpsum Amount ans select the Option That gives higher Present value

Since Present value of Annual payments are higher , Select Annuity payments

Present value = 100000*[1 - (1+8%)^-20 / 8% ]

= 981,814.74

using the same Concept above , here Present value of lumpsum Is higher So select Lumpsum Amount Of 1,000,000

Decrease In NPV when Interest rate decreases 2% = (1146992.12 - 981814.74) = 165,177.38

Indifference Interest rate = 6% + (2% / 165177.38)*(1146992.12 - 1000000) = 7.75%

So at 7.75% Interest rate you will be Indifferent

Future value = Present value*(1+r)^n

r = Periodical Interest rate = 3% / 12 = 0.25%

n = Number of periods = ?

2000000 = 1000000*(1+0.25%)^n

1.0025^n = 2

Apply Log On both sides

n Log(1.0025) = Log(2)

n = log(2) / Log(1.0025)

n = 0.3010 / 0.00108

n = 277.61 Months

n = 277.61 / 12 = 23.13 Years

EAR = (1+(APR/m))^m - 1

m = Number of Compounding periods

EAR = (1+(3%/12))^12 - 1

Effective annual rate = 3.0416%

Q2)

(a) Account balance at the end of year 10 is $115,421

Timeline for the Investment A is as follows

Month	Opening Value	Interest @8%	Closing Value
1	52000	347	52347
2	52347	349	52696
3	52696	351	53047
4	53047	354	53401
5	53401	356	53757
6	53757	358	54115
7	54115	361	54476
8	54476	363	54839
9	54839	366	55205
10	55205	368	55573
11	55573	370	55943
12	55943	373	56316
13	56316	375	56691
14	56691	378	57069
15	57069	380	57450
16	57450	383	57833
17	57833	386	58218
18	58218	388	58606
19	58606	391	58997
20	58997	393	59391
21	59391	396	59786
22	59786	399	60185
23	60185	401	60586
24	60586	404	60990
25	60990	407	61397
26	61397	409	61806
27	61806	412	62218
28	62218	415	62633
29	62633	418	63050
30	63050	420	63471
31	63471	423	63894
32	63894	426	64320
33	64320	429	64749
34	64749	432	65180
35	65180	435	65615
36	65615	437	66052
37	66052	440	66493
38	66493	443	66936
39	66936	446	67382
40	67382	449	67831
41	67831	452	68284
42	68284	455	68739
43	68739	458	69197
44	69197	461	69658
45	69658	464	70123
46	70123	467	70590
47	70590	471	71061
48	71061	474	71535
49	71535	477	72012
50	72012	480	72492
51	72492	483	72975
52	72975	486	73461
53	73461	490	73951
54	73951	493	74444
55	74444	496	74940
56	74940	500	75440
57	75440	503	75943
58	75943	506	76449
59	76449	510	76959
60	76959	513	77472
61	77472	516	77988
62	77988	520	78508
63	78508	523	79032
64	79032	527	79559
65	79559	530	80089
66	80089	534	80623
67	80623	537	81160
68	81160	541	81702
69	81702	545	82246
70	82246	548	82795
71	82795	552	83346
72	83346	556	83902
73	83902	559	84461
74	84461	563	85025
75	85025	567	85591
76	85591	571	86162
77	86162	574	86736
78	86736	578	87315
79	87315	582	87897
80	87897	586	88483
81	88483	590	89073
82	89073	594	89666
83	89666	598	90264
84	90264	602	90866
85	90866	606	91472
86	91472	610	92082
87	92082	614	92695
88	92695	618	93313
89	93313	622	93935
90	93935	626	94562
91	94562	630	95192
92	95192	635	95827
93	95827	639	96466
94	96466	643	97109
95	97109	647	97756
96	97756	652	98408
97	98408	656	99064
98	99064	660	99724
99	99724	665	100389
100	100389	669	101058
101	101058	674	101732
102	101732	678	102410
103	102410	683	103093
104	103093	687	103780
105	103780	692	104472
106	104472	696	105169
107	105169	701	105870
108	105870	706	106576
109	106576	711	107286
110	107286	715	108001
111	108001	720	108721
112	108721	725	109446
113	109446	730	110176
114	110176	735	110910
115	110910	739	111650
116	111650	744	112394
117	112394	749	113143
118	113143	754	113898
119	113898	759	114657
120	114657	764	115421

(b) Account balance at the end of year 5 is $93,699

Timeline for the Investment B is as follows

Month	Opening Value	Investment	Interest @10%	Closing Value
1	0	1200	10	1210
2	1210	1200	20	2430
3	2430	1200	30	3660
4	3660	1200	41	4901
5	4901	1200	51	6152
6	6152	1200	61	7413
7	7413	1200	72	8685
8	8685	1200	82	9967
9	9967	1200	93	11260
10	11260	1200	104	12564
11	12564	1200	115	13879
12	13879	1200	126	15204
13	15204	1200	137	16541
14	16541	1200	148	17889
15	17889	1200	159	19248
16	19248	1200	170	20618
17	20618	1200	182	22000
18	22000	1200	193	23394
19	23394	1200	205	24798
20	24798	1200	217	26215
21	26215	1200	228	27644
22	27644	1200	240	29084
23	29084	1200	252	30536
24	30536	1200	264	32001
25	32001	1200	277	33477
26	33477	1200	289	34966
27	34966	1200	301	36468
28	36468	1200	314	37982
29	37982	1200	327	39508
30	39508	1200	339	41047
31	41047	1200	352	42600
32	42600	1200	365	44165
33	44165	1200	378	45743
34	45743	1200	391	47334
35	47334	1200	404	48938
36	48938	1200	418	50556
37	50556	1200	431	52187
38	52187	1200	445	53832
39	53832	1200	459	55491
40	55491	1200	472	57163
41	57163	1200	486	58850
42	58850	1200	500	60550
43	60550	1200	515	62265
44	62265	1200	529	63993
45	63993	1200	543	65737
46	65737	1200	558	67495
47	67495	1200	572	69267
48	69267	1200	587	71054
49	71054	1200	602	72856
50	72856	1200	617	74673
51	74673	1200	632	76506
52	76506	1200	648	78353
53	78353	1200	663	80216
54	80216	1200	678	82095
55	82095	1200	694	83989
56	83989	1200	710	85899
57	85899	1200	726	87825
58	87825	1200	742	89766
59	89766	1200	758	91724
60	91724	1200	774	93699

Q3)

Part (a):

Number of 15 year coupon bonds issued 4 years ago= Total value/ Par value per bond

=30000000/1000= 30,000

Repayment at the maturity date:

Redemption of par value $30 million and one semi annual interest of 30 million*6.8%/2= 1.02 million

Total $31.02 million

Part (b):

Current price of 15 year coupon issued 4 years ago= $848.37

Calculation using TI BA II Plus calculator:

Set END

P/Y= 2, C/Y= 2

N= 11*2=22

I/Y= 9

PMT= 1000*6.8%/2= 34

FV= 1000

CPT PV= -848.3713276

Current price of 15 year zero coupon bond= $267 as follows:

N= 15*2= 30

I/Y= 9

PMT= 0

FV= 1000

CPT PV= -267

Part (c):

Number of zero coupon bonds to be issued to raise $20 million= Amount required/Price per bond

=20000000/267= 74,907 (rounded)

Repayment of zero coupon bonds at the maturity date= Number of bonds* face value per bond

=74907*1000 = $74,907,000

Part (d): Sensitivity of bond prices to interest rate changes is dependant on Duration. The more the Macaulay Duration, the more sensitive and vice versa.

Duration of zero coupon bond is its term to maturity which is 15 years.

Since the remaining term to maturity of coupon bond is 11 years, Duration is not more than 11 years.

Hence the zero coupon bond with higher duration is more sensitive

Assume that you just won the government vaccination lottery

Purchase A New Answer

Custom new solution created by our subject matter experts

GET A QUOTE

Answer Preview

Sitejabber (5.0)

Merchant Circle (4.8)

Trustpilot (4.6)

Study Help Me (4.9)

Related Questions

Address

Phone Number

Email Address