FINA2010 Classwork Lecture 3 PDF

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FINA2010L Financial Management

Classwork

Lecture 3

1. Chapter 4 Question 12 – Present Value and Cash Flows Investment X offers to pay you $4,500 per year for nine years, whereas Investment Y offers to pay you $7,000 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent? If the discount rate is 22 percent? If the discount rate is 5 percent, C 1 4500 1 present value of Investment X= × 1− = × 1− =$ 31985 T r 0.05 ( 1+ r ) ( 1+0.05 )9 1 70 00 1 C = × 1− =$ 30306 present value of InvestmentY = × 1− T 5 r 0.05 ( 1+r ) ( 1+0.05 ) Investment X has a higher present value.

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If the discount rate is 22 percent,

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C 1 4500 1 = × 1− × 1− =$ 17038 T 9 r 0. 22 ( 1+r ) ( 1+0. 22 ) C 1 70 00 1 × 1− =$ 20045 present value of Investment Y = × 1− = 5 T r 0. 22 ( 1+r ) ( 1+0. 22 ) Investment Y has a higher present value. present value of Investment X=

2. Chapter 4 Question 12 – Calculating Annuity Present Value An investment offers $4,900 per year for 15 years, with the first payment occurring one year from now. If the required return is 8 percent, what is the value of the investment? What would be the value if the payment occurred for 40 years? For 75 years? Forever?

If the payment occurred for 15 years, value of the investment=

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4900 1 × 1− =$ 41941 0. 08 ( 1+ 0. 08 )15

If the payment occurred for 40 years, value of the investment=

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4900 1 × 1− =$ 58431 40 0.08 ( 1+ 0.08 )

If the payment occurred for 75 years, value of the investment=

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4900 1 × 1− =$ 61059 75 0.08 ( 1+ 0.08 )

If the payment occurred forever, e investment=

4900 =$ 61250 0.08

3. Chapter 4 Question 21 – Future Value What is the future value in six years of $1,000 invested in an account with a stated annual interest rate of 9%, compounded (a) annually; (b) semiannually; (c) monthly; (d) continuously? (e) Why does the future value increase as the compounding period shortens?

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r m ×T 0.09 =1000 × 1+ m 1 m ×T r 0.09 =1000 × 1+ (b) FV =C 0 × 1+ m 2 m ×T 0.09 r =1000 × 1+ (c) FV =C 0 × 1+ m 12 rT 0.09 ×6 (d) FV =C 0 × e =1000 ×e =$ 1716 (a) FV =C 0 × 1+

) ) )

1× 6

=$ 1677

2× 6

=$ 1696

12× 6

=$ 17 13

(e) Shorter compounding periods implies that the principal can increase earlier....