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# Payback methods, IRR, and Right Discount Rate

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Payback Methods

8-2 Suppose that a thirty-year U.S. Treasury bond offers a 4 percent coupon rate, paid semiannually. The market price of the bond is \$1,000, equal to its par value.

a. What is the payback period for this bond?
b. With such a long payback period, is the bond a bad investment?
c. What is the discounted payback period for the bond, assuming its 4 percent coupon rate is the required return? What general principle does this example illustrate regarding a project's life, its discounted payback period, and its NPV?

Internal Rate of Return

8-9 For each of the projects shown in the following table, calculate the internal rate of return (IRR).

Project A Project B Project C Project D
Initial Cash
Outflow (CF) \$72,000 \$440,000 \$18,000 \$215,000
Year (t)
1 \$16,000 \$135,000 \$7,000 \$108,000
2 \$20,000 \$135,000 \$7,000 \$90,000
3 \$24,000 \$135,000 \$7,000 \$72,000
4 \$28,000 \$135,000 \$7,000 \$54,000
5 \$32,000 ? \$7,000 ?

Choosing the Right Discount Rate

10-1a Intel Corp. (INTC) has a capital structure consisting almost entirely of equality.
a. If the beta of INTC stock equals 1.6, the risk-free rate equals 6 percent, and the expected return on the market portfolio equals 11 percent, what is INTC's cost of equity?

10-3 In its 2006 annual report, The Coca-Cola Company reported sales of \$24.09 billion for fiscal year 2006 and \$23.10 billion for fiscal year 2005. The company also reported operating income (roughly equivalent) to EBIT) of \$6.31 billion, and \$6.09 billion in 2005 and 2006, respectively. Meanwhile, arch-rival PEPsi Co, Inc. reported sales of \$35.14 billion in 2006 and #32.56 billion in 2005. PepsiCo's operating profit was \$6.44 billion in 2006 and \$5.92 billion in 2005. Based on these figures, which company had higher operating leverage?

#### Solution Preview

Payback Methods

8-2 Suppose that a thirty-year U.S. Treasury bond offers a 4 percent coupon rate, paid semiannually. The market price of the bond is \$1,000, equal to its par value.

a. What is the payback period for this bond?

Coupon received per year = \$1,000 x 4% = \$40 per year

Payback period is defined as the expected number of years required to recover the original investment.

Payback Period = Initial Amount/Cash flow received each year
= \$1,000/\$40
= 25 years

b. With such a long payback period, is the bond a bad investment?

It depends on the objective of the investors. If they are risk-averse and their required rate of return is only 4%, then the bond is not a bad investment. However, if the objective of the investors is to invest in short payback period, then the bond is a bad investment.

c. What is the discounted payback period for the bond, assuming its 4 percent coupon rate is the required return? What general principle does this example illustrate regarding a project's life, its discounted payback period, and its NPV?

First you have to find the present value of cash flow year 1 to 30 using 4% and then find the payback period. However, please note that the discounted will be based on semiannual coupon ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer what is the payback period for this bond, is the bond a bad investment with such a long payback period, what is the discounted payback period for the bond, assuming its 4 percent coupon rate is the required return, what general principle does this example illustrate regarding a project's life, its discounted payback period, and its NPV, calculate the internal rate of return (IRR) for each projects, what is INTC's cost of equity, and which company had higher operating leverage.

\$2.19