Question

Assuming semiannual compounding, a 10-year zero coupon bond with a par value of $1,000 and a required return of 11.8% would be priced at _________.

$317.75

$327.78

$894.45

$944.29

Answer 1

Correct answer is A

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Since the compounding is done semi-annually, lets calculate effective interest first.

The effective annual interest rate is the interest rate that is actually earned or paid on an investment, loan or other financial product due to the result of compounding over a given time period. It is also called the effective interest rate, the effective rate or the annual equivalent rate

So if nominal interest rate (i), number of compounding in a year is (m), effective interest will be

Effective interest rate = (1 + i/m) ^m -1

Where,

Nominal interest rate (i) = 11.8% per year

Number of compounding in a year (m) = 2

Let's put all the values in the formula

Effective interest rate = (1 + 0.118/2) ^2 - 1

                                              = (1 + 0.059) ^2 - 1

                                              = (1.059) ^2 - 1

                                              = 1.12148 - 1

                                              = 0.12148

So annual effective interest rate is 12.15% per year

Now we can calculate PV of bond using PV of sum.

Present value is the present worth of cash that is to be received in the future, if future value is known, rate of interest in r and time is n then PV is

PV = FV/ (1 + r) ^n

Where,

FV = 1000

r = 0.12148

n = 10

Let's put all the values in the formula

= 1000/ (1 + 0.12148)^10

= 1000/ (1.12148)^10

= 1000/ 3.1471

= 317.75

Price of the bond is 317.75

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