Calculate the price at each call date an d the maturity date ...
MATH 373 Test 3
Fall 2017
November 16, 2017
1. Jackson purchases a callable bond. The bond matures at the end of 20 years for 52,000. The bond pays semi-annual coupons of 1300.
The bond can be called at the end of 14 years. The call value is 54,925. The bond can be called at the end of 16 years. The call value is 53,950. The bond can be called at the end of 18 years. The call value is 52,975.
Jackson buys the bond to yield 4% convertible semi-annually.
Determine the price of the bond.
Solution:
Calculate the price at each call date and the maturity date and pick the lowest price.
I / Y 4% / 2 2; PMT 1300
N FV
PV
28 54,925 59,123.20
32 53,950 59,136.50
36 52,975 59,105.07 40 52, 000 59,112.42
May 1, 2018 Copyright Jeffrey Beckley 2017, 2018
2. The common stock of Zhang Corporation pays a quarterly dividend. The next dividend of 5.00 will be paid in one month. Future dividends are expected to increase such that each dividend is
2% greater than the prior dividend. In other words, a dividend of 5.00 will be paid at the end of one month. A dividend of 5.00(1.02) will be paid at the end of 4 months. A dividend of 5.00(1.02)2 will be paid at the end of 7 months, etc.
Using the dividend discount method, determine the price that Summer should pay in order to have an annual effective return of 12%.
Solution:
PV 5(1.12)1/12 5(1.02)(1.12)4/12 ...
5(1.12)1/12
583.17
1 (1.02)(1.12)3/12
May 1, 2018 Copyright Jeffrey Beckley 2017, 2018
3. Wendy is the beneficiary of an annuity due which makes monthly payments for 15 years. Each monthly payment in the first year are 1000. Each monthly payment in the second year is 2000. The payments continue to increase until each monthly payment in the 15th year is 15,000.
Calculate the present value of Wendy's annuity at an interest rate of 9% compounded monthly.
Solution:
We have to use the formula that does not follow the rules since the payments are level during each year but increase year to year. We also note that this is an annuity due.
PV
1000
a 15 i
15(1 i)15 i (12 ) 12
1
i (12 ) 12
i(12) 0.09 0.0075
and
i (1.0075)12 1 0.093806898
12 12
PV
1000
1 (1.093806898)15
0.093806898
(1.093806898)
0.0075
15(1.093806898)15
1.0075
633, 233.59
May 1, 2018 Copyright Jeffrey Beckley 2017, 2018
4. A continuous perpetuity that pays at a rate of 1000t at time t has a present value of 25,000 when calculated at a force of interest of .
Chengjia is receiving a continuous 20 year annuity that pays at a rate of 500t at time t .
Calculate the present value of Chengjia's annuity using a force of interest equal to 0.5 which is
one half the force of interest used to calculate the present value of the perpetuity. Solution:
We will use the perpetuity to find .
25, 000
1000 2
2
1 25
0.2
Now we will find the present value of the annuity at 0.5 0.10
PV
(500)
a 20
20e20( )
(500)
1 e20(0.1) 20e20(0.1) 0.1 0.1
29, 699.71
May 1, 2018 Copyright Jeffrey Beckley 2017, 2018
5. Tom purchases a 2 year bond which matures for 20,000. The bond has semi-annual coupons. The coupons are not level. The first two coupons are each equal to 1000. The second two coupons are each equal to 2000.
The bond is bought to yield 13% convertible semi-annually.
Complete the following amortization table for Tom's bond. Show formulas if you want full credit.
Time k Coupon Interest in Coupon Principal in Coupon
Book Value
0
---
---
Present Value of Cash
Flows =
---
1000v+1000v2+2000v3
+(2000+20000)v4
=20,577.43
1
1000
(20,577.43)(0.065) = 1337.53
1000 ? 1337.53 = -337.53
20,577.43 ? (-337.53) =20,914.96
2
1000
(20,914.96)(0.065) = 1359.79
1000 ? 1359.47 = -359.47
20,914.96 ? (-359.47) =21,277.43
3
2000
(21,277.43)(0.065) = 1382.84
2000 ? 1382.84 = 617.16
21,277.43 ? 617.16 = 20,657.27
4
2000
(20,657.27)(0.065) = 1342.72
2000 ? 1342.72 = 657.28
20,657.27 ? 657.28 = 20,000
May 1, 2018 Copyright Jeffrey Beckley 2017, 2018
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