Crane, Inc., has bonds outstanding that will mature in 8 years. The bonds have a face...

Crane, Inc., has bonds outstanding that will mature in 8 years. The bonds have a face value of $1,000. These bonds pay interest semiannually and have a coupon rate of 4.6 percent. If the bonds are currently selling at $867.92, what is the yield to maturity that an investor who buys them today can expect to earn? (Round answer to 3 decimal place, e.g. 5.275%.)

Yield to maturity = (in %)

What is the effective annual yield? (in %)

Solutions

Expert Solution

Face value of bond is 1000

Coupon rate is 4.6%

Paid semiannualy so periodic interest is = 4.6/2 = 2.3%

No of periods to maturity is 16 periods (8×2)

Current rate is 867.92

Calculation

Yield to maturity: it is defined as yield we realise on bond if we hold that bond till maturity

We use interpolation method to calculate the yield to maturity

When coupon rate is equal is to market price will be equal to face value when market rate is 2.3%

Value of bond when periodic interest is 3.3%

Value of bond is present value of cash flows

= 23(PVIFA 3.3% 16p) + 1000(PVIF 3.3%% 16p)

= 23(12.2778) + 1000(0.5848)= 867.18

So when yield is (3.3×2)= 6.6% bond price is equal to market value. We generally use interpolation method to calculate it but our random discount rate matched with price

So yield to maturity is = 6.6%

B) equivalent yield is = coupon rate /Market price

= 46/867.92 = 5.3%(also known as current yield)

jeff jeffy answered 1 year ago

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