Question

11. At a discount rate of 5%, what is worth the MOST: $50 received today, $55 received in 1 year, or $65 received in 3 years? Please show your work.

12. Would it ever make any sense to pay $1,200 for an 8% coupon bond with a face value of $1,000? Explain.

Answer 1

11. Discount rate = r = 5%

Option 1: $50 received today will have a present value of $50

Option 2: $55 received in 1 year,

Present value = PV = 55/(1+5%)¹ = 55/1.05 = 52.3809523809524

$55 received after 1 year will have a present value of $52.38

Option 3: $65 received in 3 years

Present value = 65/(1+5%)³ = 65/1.05³ = 56.1494439045459

The present value of $65 received in 3 years will be $56.15

We can see that the present value of option 3 i.e., $65 received in 3 years is the maximum. So, it has got the most worth

Answer -> $65 received in 3 years

12. Yes, it will depend on the maturity and the YTM of the bond. YTM of the bond should be less than 8% (coupon rate) as it is trading a premium. If a bond's coupon rate is greater than its yield to maturity then the bond trades at a premium price (which is greater than its face value). So, the maturity and the YTM of the bond will together decide its current price at which it is trading. If the current price comes out to be $1200 then it makes sense to pay $1200 for an 8% coupon bond with a face value of $1000