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MBA711 - Answers to Book - Chapter 5

MBA711 - Answers to Book - Chapter 5 - Chapter 5 Solutions...

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Chapter 5, Solutions Cornett, Adair, and Nofsinger CHAPTER 5 – Time Value of Money 2: ANALYZING ANNUITY CASH FLOWS Questions LG1 5-1 How can you add a cash flow in year two and a cash flow in year four in year seven? To add cash flows, they need to be moved to the same time period. The cash flows in years two and four should be moved forward with interest to year seven, then they can be added together. LG2 5-2 People can become millionaires in their retirement years quite easily if they start saving early in employer 401(k) or 403(b) programs (or even if their employers don’t offer such programs). Demonstrate the growth of a \$250 monthly contribution for 40 years earning 9 percent APR. Using equation 5-2, we have: ( 29 07 . 330 , 170 , 1 \$ 0.09/12 1 12 / 09 . 0 1 250 FVA 480 40 = - + × = LG3 5-3 When you discount multiple cash flows, how does the future period that a cash flow is paid affect its present value and its contribution to the value of all the cash flows? Discounting reduces a future cash flow to a smaller present value. Cash flows far into the future become very small when discounted to the present. Thus, cash flows in distant future periods have small impacts on present values. LG4 5-4 How can you use the present value of an annuity concept to determine the price of a house you can afford? Mortgages are typically for a large enough amount of money that borrowing is required to purchase a home. The amount that one can afford for a home is a function of their current state of wealth. Mortgages allow consumers to spread the expense of a home over a longer period, typically 15 or 30 years. This allows consumers to put a smaller portion of wealth into the home (for example, a 20% down payment) and borrow the balance over the life of the loan. Due to the effect of annuity compounding, the payments for such a long lived debt make the monthly payments of a manageable nature so that they can be paid from current income. LG5 5-5 Since perpetuity payments continue for ever, how can a present value be computed? Why isn’t the present value infinite? 5-1

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Chapter 5, Solutions Cornett, Adair, and Nofsinger Equation 5-5 is used to calculate the present value of a perpetuity. It is a limiting version of equation 5-4 in which the period N grows infinitely large. As this occurs the expression following the “1” in equation 5-4 drives to the value 0 and the numerator simply become “1.” The present value is not infinite since the terms following the PMT in equation 5-4 converge to a finite limit of 1/i. This also demonstrates how payments far into the future have infinitesimal value today. LG6 5-6 Explain why you use the same adjustment factor, (1 + i ), when you adjust annuity due payments for both future value and present value. Adjusting an annuity due calculation involves shifting the entire series of payments forward one period. This is accomplished by multiplying by (1 + i) irrespective of whether it is a future value or present value calculation.
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