Crane Company issues $5040000, 7%, 5-year bonds dated January 1, 2020 on January 1, 2020. The...

Crane Company issues $5040000, 7%, 5-year bonds dated January 1, 2020 on January 1, 2020. The bonds pay interest semiannually on June 30 and December 31. The bonds are issued to yield 6%. What are the proceeds from the bond issue?

ff	3.0%	3.5%	6%	7%
Present value of a single sum for 5 periods	0.86261	0.84197	0.74726	0.71299
Present value of a single sum for 10 periods	0.74409	0.70892	0.55839	0.50835
Present value of an annuity for 5 periods	4.57971	4.51505	4.21236	4.10020
Present value of an annuity for 10 periods	8.53020	8.31661	7.36009	7.02358

$5040000

$5254941

$5253441

$5252626

Solutions

Expert Solution

Option (b) is correct

Bond proceeds are the price of the bond. It can be calculated by the following formula:

Bond price = Present value of interest payment + Present value of bond payment at maturity

Semi annual bond interest = 7% * $5040000 * 1/2 = $176400

Bond interest payments will be semi annual every year, so it is an annuity. While calculating the present value of bond interest payment, we will use the present value of annuity (PVA) of $1 table and bond payment at maturity is a one time payment, so we will use the present value (PV) of $1 table. The interest rate that will be used in calculating the required present values will be the semi annual yield, which is 6% /2 = 3%, with 5*2 = 10 periods.

Now,

Bond price = $176400 * PVA (3%, 10 years) + $5040000 * PV (3%, 10 years)

We will now find the values of PVA (3%, 10 years) and PV (3%, 10 years) from the table given and solve this equation.

Bond price = ($176400 * 8.530208) + ($5040000 * 0.744090)

Bond price = $1504728.6912 + $3750213.6

Bond price = $5254941

So, bond proceeds are $5254941.

ekkarill92 answered 1 year ago

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