Chapter4 - Chapter 4 Solutions 2 You have just won $10...

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Chapter 4 Solutions 2. You have just won $10 million in the state lottery which promises to pay you $1 million (tax free) every year for the next ten years. Have you really won $10 million? No, because the present discounted value of these payments is necessarily less than $10 million as long as the interest rate is greater than zero. 3. If the interest rate is 10%, what is the present value of a security that pays you $1,100 next year, $1,210 the year after, and $1,331 the year after that? PV = FV 1 /(1+i) + FV 2 /(1+i) 2 + FV 3 /(1+i) 3 PV = $1,100/1.1 + $1,210/1.1 2 + $1,331/1.1 3 = $3,000 5. Write down the formula that is used to calculate the yield to maturity on a twenty-year 10% coupon bond with $1,000 face value that sells for $2,000. The present value is the purchase price of $2,000. The future value is the face value of $1,000. The annual coupon payment is 10% of the face-value, or $100. The bond term is 20 years. The present value formula for a coupon bond is: PV = C/(1+i) + C/(1+i) 2 + … + C/(1+i) n + F/(1+i) n Plugging in the above information gives: $2,000 = $100/(1+i) + $100/(1+i) 2 + … + $100/(1+i) 20 + $1000/(1+i) 20 Using a financial calculator, you could find the yield to maturity as i = 3%.
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