Question

Problem 5-16 Calculating Rates of Return [LO3] Rust Bucket Motor Credit Corporation (RBMCC), a subsidiary of Rust Bucket Motor, offered some securities of one of these securities $100,000 on March 28, 2039, but investors would receive nothing until then. Investors paid RBMCC $24,599 for each of these securities; so they gave up $24,599 on March 28, 2008, for the promise of a $100,000 payment 31 years later. a. Based on the $24,599 price, what rate was RBMCC paying to borrow money? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Rate of return b. Suppose that, on March 28, 2018, this security's price is $42,880. If an investor had purchased it for $24,599 at the offering and sold it on this day, what annual rate of return would she have earned? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Annual rate of return c. If an investor had purchased the security at market on March 28, 2018, and held it until it matured, what annual rate of return would she have earned? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16) Annual rate of return 4.11 %

Answer 1

(a) Current Price = $ 24599 and Final Redemption Price = $ 100000, Investment Tenure = 31 years

Let the borrowing rate (annual interest rate) be R

Therefore, 24599 = 100000 / (1+R)^(31)

R = 0.04628 or 4.63 %

(b) Current Price = $ 24599 and Final Selling Price = $ 42880, Investment Tenure = 10 years

Let the annual rate of return earned be R1

Therefore, 24599 = 42880 / (1+R1)^(10)

R1 = 0.057143 or 5.71 %

(c) Buying Price = $ 42880, Final Redemption Price = $ 100000 and Tenure = 21 years

Let the annual rate of return earned be R2

Therefore, 42880 = 100000 / (1+R2)^(21)

R2 = 0.04115 or 4.11 %