Question

Time Value of Money and Bonds Valuation

As Laura’s new year resolution, she wants to begin saving money for her retirement. You are hired as her financial advisor. Following your suggestion, today Michelle will deposit $100,000, which she inherited from her parents, into a 5-year savings account at Citi bank, which pays 3.25% interest annually.

Use the above information to answer the following questions. When answering your question, make sure to include the calculation steps or formula. (Assume END mode)

5. Assume after 5 years, Laura will be 40 years old and will have $150,000 in her saving account, and she is planning to retire at 65 years old and she will need $1,000,000 at retirement. What annual interest rate must she earn to reach her goal, assuming each year she will only save $20,000.

Laura asks you to help her invest in the bonds market. You have the following three bonds good for investment. Assume all coupons are paid annually and END mode, find the best option for your friend?

Option One: Treasury bond has 4% annual coupon, matures in 10 years, and has a $10,000 face value. Its price is $9,550

Option Two: Corporate Bond A has a 9% annual coupon, matures in 5 years, and has a $10,000 face value. Its price is $10,500

Option Three: Corporate Bond B has a 10% annual coupon, matures in 8 years, and has a $10,000 face value. Its price is $9,950

5. Calculate YTM for each bond.

6. Compare YTM with coupon rate, indicate whether each bond is trading at a premium, at a discount, or almost at par.

7. Which one do you recommend Michelle to buy and why, assume Michelle has a high-risk tolerance and the current market interest rate is around 6%, Corporate Bond A is rated as BB bond and Corporate Bond B is a high-yield risky bond?

8. Assume Laura also told you her expected residual savings from 2019 to 2023 will be: $15,000, $20,000, $25,000, $30,000, $35,000. She wants to know the present values of these savings at an 8% discount rate. Calculate PVs of the streams.

Answer 1

5. Assume after 5 years, Laura will be 40 years old and will have $150,000 in her saving account, and she is planning to retire at 65 years old and she will need $1,000,000 at retirement. What annual interest rate must she earn to reach her goal, assuming each year she will only save $20,000.

PV=-150000

FV=1000000

N=25

PMT=-20000

CPT I/Y=2.742%

Laura asks you to help her invest in the bonds market. You have the following three bonds good for investment. Assume all coupons are paid annually and END mode, find the best option for your friend?

Option One: Treasury bond has 4% annual coupon, matures in 10 years, and has a $10,000 face value. Its price is $9,550

PMT=4%*10000

PV=-9550

FV=10000

N=10

CPT I/Y=4.571%

Option Two: Corporate Bond A has a 9% annual coupon, matures in 5 years, and has a $10,000 face value. Its price is $10,500

PMT=9%*10000

PV=-10500

FV=10000

N=5

CPT I/Y=7.756%

Option Three: Corporate Bond B has a 10% annual coupon, matures in 8 years, and has a $10,000 face value. Its price is $9,950

PMT=10%*10000

PV=-9950

FV=10000

N=8

CPT I/Y=10.094%

6. Compare YTM with coupon rate, indicate whether each bond is trading at a premium, at a discount, or almost at par.

A bond trades at premium when ytm is less than coupon rate and at discount when ytm is more than coupon rate

Treasury Bond is trading at discount

Corporate Bond A is trading at premium

Corporate Bond B is trading at discount

7. Which one do you recommend Michelle to buy and why, assume Michelle has a high-risk tolerance and the current market interest rate is around 6%, Corporate Bond A is rated as BB bond and Corporate Bond B is a high-yield risky bond?

Depends on default risk spread

But it seems she should buy Bond A assuming default risk premium between high yield risky bond is same as default risk premium between BB bond and Treasury Bond

8. Assume Laura also told you her expected residual savings from 2019 to 2023 will be: $15,000, $20,000, $25,000, $30,000, $35,000. She wants to know the present values of these savings at an 8% discount rate. Calculate PVs of the streams.

=15000/1.08+20000/1.08^2+25000/1.08^3+30000/1.08^4+35000/1.08^5=96752.7788