Final answer:
The manufacturer's rate of return is calculated by determining the present value of all cash inflows and outflows related to the manufacturing plant investment, considering the issuance of bonds and increasing profits. The calculation involves discounting each future profit and bond payment by the bond's interest rate and finding the rate of return that balances the investment costs with cash flows.
Step-by-step explanation:
The question asks us to calculate the manufacturer's rate of return on an investment in a manufacturing plant over an 8-year period, considering the issuance of tax-free industrial revenue bonds and the projected profit growth from the plant's operations. To find the rate of return, we would sum the present values of all cash inflows (profits from the plant) and outflows (interest payments, principal repayment) and compare them to the initial investment of $20 million. Profits are said to be $3 million at the end of the second year and grow by 10% each year thereafter. The interest on the bonds is 8% per annum.
For example, to find the present value of the profit in year three (which is the end of year two's profit growing by 10%), we would use the formula PV = FV / (1+r)^n, where FV is the future value of the profit, r is the discount rate (8% or 0.08) and n is the number of years until the payment. Similarly, we would calculate the present value of profits for subsequent years and the present value of bond interest payments and principal repayment. However, the exact numerical value for the manufacturer's rate of return would be determined by setting the net present value of the investment to zero and solving for the rate that equates the cash inflows and outflows, which typically requires financial calculations using more advanced methods like the internal rate of return (IRR).