Your friend recommends that you invest in a three-year bond issued by Trimer, Inc., that will pay annual coupons of 10 percent. Similar investments today will yield 6 percent. How much should you pay for the bond? (Do not round intermediate computations. Round your final answer to the nearest dollar.)

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Quizplus · Accepted Answer

The value of the bond can be calculated using the present value of its future cash flows, which include the annual coupon payments and the principal amount at maturity. The formula for the present value of an annuity (the coupon payments) plus the present value of a lump sum (the principal repayment) is used here. Given a 10% annual coupon on a bond with a face value of $1,000 (commonly the case unless stated otherwise), the annual coupon payment is $100. The discount rate (current market yield) is 6%. The bond has 3 years until maturity.The present value of the annual coupon payments (Annuity) can be calculated using the formula: PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the annual payment ($100), r is the annual discount rate (0.06), and n is the number of periods (3 years). PV of coupons = $100 * [(1 - (1 + 0.06)^-3) / 0.06] = $100 * [1 - (1.06)^-3] / 0.06 ≈ $267.645The present value of the principal amount (Lump Sum) is calculated using the formula: PV = F / (1 + r)^n, where F is the face value ($1,000), r is the annual discount rate (0.06), and n is the number of periods (3 years).PV of principal = $1,000 / (1 + 0.06)^3 ≈ $839.62Adding the present value of the coupons and the principal gives the total present value of the bond:Total PV = PV of coupons + PV of principal ≈ $267.645 + $839.62 ≈ $1,107.27Rounded to the nearest dollar, the price you should pay for the bond is approximately $1,107.

Your Friend Recommends That You Invest in a Three-Year Bond