Future Values of Investments and Annuities

Discussion Questions

1. Present values are negatively impacted by higher interest rates. How does compounding compare with discounting? How does the future value of an annuity compare with the future value of a lump sum? 

Compounding is different from discounting as it is used to find the future value of a present value by using the compound interest rate. On the contrary, discounting is used to find the present value of a given future value by using a discount rate. The accounting relationship between compounding and discounting is mathematically inverse. 

The future value of an annuity and the future value of a lump sum are different in nature. The future value of an annuity is the calculated value of a set of payments in the future. Annuity is simply another name for payments. The future value of an annuity calculates how much cash value can be measured in the future when given an interest or discount rate. The future value of a lump sum is different; in that, there is not a set of payments attached to the calculation. The future value of an annuity and the future value of a lump sum have two different mathematical formulas. Both formulas, however, are successful in showing the time value of money and the impact of interest on both annuities and lump sums (Lubbock). 

2. Long-term bonds face interest-rate risk; short-term bonds face reinvestment-rate risk. How is the value of a typical corporate bond determined? 

Bonds have several characteristics that work in concert to support valuation. The face value of a bond is the amount of cash a bondholder will receive at the date of maturity. The maturity date is the specific time that the principal will be repaid. Interest is paid over the course of the bond’s life, usually every six months. Interest is the amount that will be paid to the investor. The bond coupon is the amount the investor will receive in interest. The variables to the equation are face value, interest, maturity, and number and nature of interest payments (every month, 6 months, year?). The amount of interest expected reflects the bond risk. A high-risk company that issues a bond will pay more interest while a blue-chip company will pay lower interest and coupon (Brennan & Schwarts).

3. It is important for managers to accept positive NPV projects. What are some problems with the IRR methodology compared to the NPV methodology?

Capital budgeting uses NPV and IRR methodologies to decide if investment opportunities are financially responsible. To make the best decision under the time value of money constraints a business will calculate the future cash flow and then discount that amount using a present value calculation. The value of the project’s future cash receipts is discounted to a single present value. By subtracting this value from the original investment, a business can determine if the investment is viable. IRR uses one discount rate to calculate the benefit of every opportunity. IRR is considered to be much easier to calculate; however, the complex nature of some investments lends themselves to NPV calculations. In addition, interest rates usually vary over the course of time. IRR does not factor those fluctuations so it’s not as accurate for projects that extend over a single year. While IRR may be the best option for simple, short-term calculations, it is usually the best option to use NPV methods (Ross).

Works Cited

J. W. Lubbock. The Assurance Magazine, and Journal of the Institute of Actuaries, (1855) Vol. 5, No. 3 pp. 197-207

Michael J. Brennan and Eduardo S. Schwartz. “Bond Pricing and Market Efficiency.” Financial Analysts Journal, (1982). Vol. 38, No. 5, pp. 49-56

Stephen A. Ross. “Uses, Abuses, and Alternatives to the Net Present Value Rule.” Financial Management. Vol. 24, No. 3 (Autumn, 1995), pp. 96-102