# Payback methods, IRR, and Right Discount Rate

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?

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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?

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.

NPV, IRR, and Payback

CU Boxes Inc. makes boxes for shoe manufacturers. One of the machines that CU uses may need replacement. The following information is available to you:

Revenues will not change if the machine is replaced.

Both the present machine and the new machine will last 5 years and will have no disposal value in five years.

The new machine will cost $2,000,000. The old machine can be disposed of right now for a disposal value of $60,000.

The new machine will reduce operating costs by $600,000 per year (assume cash flows at the end of the years.)

Assume a required rate of return or discount rate of 9%

Part 1: Determine if the new machine should be purchased. Use NPV, IRR, and Payback in your analysis where appropriate.

Part 2: What method (NPV or others) is the best method to use for capital budgeting purposes? Defend your arguments carefully, and take into account the following among other concerns:

a) Ease of use

b) Quality of information from such method

c) Quantity of information from such method