Question

A $1,000 par value bond was issued 25 years ago at a 12 percent coupon rate. It currently has 15 years remaining to maturity. Interest rates on similar obligations are now 10 percent. Assume Ms. Bright bought the bond three years ago when it had a price of $1,060. Further assume Ms. Bright paid 40 percent of the purchase price in cash and borrowed the rest (known as buying on margin). She used the interest payments from the bond to cover the interest costs on the loan.

a. What is the current price of the bond? (Input answer to 2 decimal places.)
b. What is her dollar profit based on the bond's current price? (Do not round intermediate calculations and round answer to 2 decimal places.)c. How much of the purchase price of $1,060 did Ms. Bright pay in cash? (Do not round intermediate calculations and round answer to 2 decimal places.)

Answer 1

A.) $1,152.12

B.) $92.12

C.) $424.00

Step-by-step explanation:

Given

period (t) = 15 years

Coupon rate = 12%

Rate (r) = 10%

Par value = $1000

Purchase price = $1060

A.) Current price of bond :

Price = Coupon payment × [(1 - (1 + r)^-t) /r] + [par value / (1+r)^t]

Coupon payment = 12% × 1000 = $120

Plugging our values

Price = 120 × [(1-(1+0.1)^-15)/0.1] + [1000/1.1^15]

Price = $1,152.12

B.) Dollar profit on bond

Dollar profit = Current price - Purchase price

Dollar profit = $1,152.12 - $1060 = $92.12

C.)Amount paid in cash

40% of purchase amount was paid in cash

0.4 × 1060 = $424.00

Answer 2

a) $1,153.72

b) $93.72

c) $424

Step-by-step explanation:

Given:

Original bond was issued at 12%

YTM = 10%

Years left, N = 15 years.

a) The current price of bond:

Using Excel function, we have:

=PV(10%/2,2*15,-12%*1000/2,-1000)

= $1153.72

The current price of bond is $1,153.72

b) Dollar profit based on bond's current price will be calculated as:

Bond's current price - purchase price

= $1,153.72 - $1,060

= $93.72

Dollar profit = $93.72

c) The purchase price of $1,060 Ms. Bright paid in cash will be:

$1,060 * 40%

= $424