MATH 373 Test 3 Fall 2017 November 16, 2017

Transcription

1 MATH 373 Test 3 Fall 2017 November 16, Jackson purchases a callable bond. The bond matures at the end of 20 years for 52,000. The bond pays semi-annual coupons of 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. 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, ,950 59, ,975 59, , ,

2 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 (1.02) 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%. PV 1/12 4/12 5(1.12) 5(1.02)(1.12)... 1/12 5(1.12) 1 (1.02)(1.12) 3/

3 3. Wendy is the beneficiary of an annuity due which makes monthly payments for 15 years. Each monthly payment in the first year are Each monthly payment in the second year is The payments continue to increase until each monthly payment in the 15 th year is 15,000. Calculate the present value of Wendy s annuity at an interest rate of 9% compounded monthly. 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 a 15 (12) 15(1 i) 15 i 1 (12) i 1000 i (12) i and i (1.0075) PV 15 1 ( ) 15 ( ) 15( ) ,

4 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. We will use the perpetuity to find , Now we will find the present value of the annuity at PV 20(0.1) 1 e 20(0.1) 20( ) a 20e 20e 20 (500) (500) ,

5 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 The second two coupons are each equal to 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 Present Value of Cash Flows = 1000v+1000v v 3 +( )v 4 =20, (20,577.43)(0.065) = = , ( ) =20, (20,914.96)(0.065) = = , ( ) =21, (21,277.43)(0.065) = = , = 20, (20,657.27)(0.065) = = , = 20,000

6 6. A 20 year loan is being repaid with 20 annual non-level payments. The first payment is 25,000. The second payment is 24,000. The payments continue to decrease until the last payment of 6000 is paid. The interest rate on the loan is an annual effective rate of 6%. Calculate the principal in the 11 th payment. We want to find the outstanding loan balance at time OLB 10 (15, 000) a a 10(1.06) 80, I OLB (0.06) (80, )(0.06) P 15, ,

7 7. Kanishk can purchase either of the following two bonds: a. Bond A has a par value of 25,000 and semi-annual coupons. The bond sells for 30,000. The coupon rate is 6% convertible semi-annually. The amount of principal in the first coupon is b. Bond B is a 20 year zero coupon bond. This bond also has a price of 30,000. Bond A and Bond B have the same yield rate. Calculate the maturity value of Bond B. BV 0 Price 30, 000 Coupon (25, 000)(0.06 / 2) 750 I Coupon P but I ( BV ) r (30, 000)( r) r , (2) Price of Bond B = (Maturity Value)(1 r) since r is for a six month perio d. 40 Maturity Value (30, 000)( ) 73,370.70

8 8. Connor buys a 12 year bond with a par value of F. The bond matures for F 500. The bond has semi-annual coupons paid at a rate of 7% convertible semi-annually. At yield rate of 9% compounded semi-annually, bond is bought at a discount of 400. Determine F. C P 400 P C 400 C F 500 P F F 100 P Fra Cv (1.045) F 100 ( F)(0.07 / 2) ( F 500)(1.045) (500)(1.045) F 24 1 (1.045) 1 (0.07 / 2) (1.045)

9 9. A 10 year bond pays semi-annual coupons that are increasing. The first coupon is 500. The second coupon is 600. The third coupon is 700. The coupons continue to increase in the same pattern. The bond has a maturity value of 13,000. Calculate the price of the bond to yield 10% convertible semi-annually. The price is the present value of cash flows. Since each coupon is increasing, we must use the P&Q formula. 100 PV 500a 20 a 20(1.05) 20 (13, 000)(1.05) (1.05) (1.05) (1.05) (13, 000)(1.05) ,979.51

10 10. Yuchen has a loan which is being repaid with level monthly payments of 500. The interest in the 30 th payment is The principal in the 36 th payment is Determine the amount of the loan. Principal in 30th Payment P P30(1 i) P (1 i) i P P (1 i) P (1.007) I OLB ( i) OLB (0.007) Amount of Loan OLB0 26, If you carry more decimals or do the problem a different way, your answer will be slightly different.

11 11. Chufan is considering the following two investments: a. A preferred stock issued by Osborn LTD. The preferred stock pays quarterly dividends of 25 with the next dividend payable later today. The price of the stock is b. A bond issued by Johnson Inc. The bond has a par value of The dividends are paid semi-annually at a rate of 8.6% compounded semi-annually. The bond matures for 1500 at the end of 20 years. The preferred stock of Osborn LTD and the bond of Johnsons Inc are expected to provide the same annual effective interest rate. Determine the price of the bond. From the stock, (4) (4) 25 i 25 i 25 Price= (4) (4) i 4 i (4) i i i i 2 2 (2) (2) But we need for the bond so (1 i) 1 ( ) ( ) 40 P (1000)(0.086 / 2) 1500( ) or PMT (1000)(0.043) 43; FV 1500; I / Y ; N 40 CPT PV

12 12. Lin has the choice of the following two loans: a. An 10 year amortization loan for 100,000 from the Bank of Senese which requires annual payments based on an annual effective interest rate 9.25%. b. A sinking fund loan from Pitman Bank. The amount of the loan is 100,000 and must be repaid over 10 years. At the end of each year, Lin would pay interest to Pitman Bank at an annual effective interest rate of i. Additionally, Lin would have to make a deposit into a sinking fund at the end of each year so that the amount in the sinking fund would exactly repay the loan at the end of 10 years. The sinking fund will earn an annual effective interest rate of 7%. The annual payment under the loan from the Bank of Senese is equal to the total of the interest payment and sinking fund deposit under the loan from Pitman Bank. Determine i For the amortization loan, we find the payment as 100, , 000 Q 15, a 1 (1.0925) For the sinking fund loan, we have two payments ==> I and D I il i(100, 000) 100, , 000 D s (1.07) , , i(100, 000) i , 000