Suppose a firm will need $100,000 20 years from now to replace some equipment. It plans to make 20 equal payments, starting today, into an investment fund. It can buy bonds that mature in 20 years or bonds that mature in 1 year. Both types of bonds currently sell to yield 10%, i.e., rd = YTM = 10%. The company’s best estimate of future interest rates is that they will stay at current levels, i.e., they may rise or they may fall, but the expected rd is the current rd.

There is some chance that the equipment will wear out in less than 20 years, in which case the company will need to cash out its investment before 20 years. If this occurs, the company will desperately need the money that has been accumulated—this money could save the business. How much should the firm plan to invest each year?