PROBLEM 5 Consider another uneven cash flow stream: Year Cash Flow 0 $2,000 1 $2
ID: 2777903 • Letter: P
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PROBLEM 5 Consider another uneven cash flow stream: Year Cash Flow 0 $2,000 1 $2,000 2 $0 3 $1,500 4 $2,500 5 $4,000 a. What is the present (Year 0) value of the cash flow stream if the opportunity cost rate is 10 percent? b. What is the value of the cash flow stream at the end of Year 5 if the cash flows are invested in an account that pays 10 percent annually? c. What cash flow today (Year 0), in lieu of the $2,000 cash flow, would be needed to accumulate $20,000 at the end of Year 5? (Assume that the cash flows for Years 1 through 5 remain the same.) d. Time value analysis involves either discounting or compounding cash flows. Many healthcare financial management decisions—such as bond refunding, capital investment, and lease versus buy—involve discounting projected future cash flows. What factors must executives consider when choosing a discount rate to apply to forecasted cash flows? ANSWER PROBLEM 5 Consider another uneven cash flow stream: Year Cash Flow 0 $2,000 1 $2,000 2 $0 3 $1,500 4 $2,500 5 $4,000 a. What is the present (Year 0) value of the cash flow stream if the opportunity cost rate is 10 percent? b. What is the value of the cash flow stream at the end of Year 5 if the cash flows are invested in an account that pays 10 percent annually? c. What cash flow today (Year 0), in lieu of the $2,000 cash flow, would be needed to accumulate $20,000 at the end of Year 5? (Assume that the cash flows for Years 1 through 5 remain the same.) d. Time value analysis involves either discounting or compounding cash flows. Many healthcare financial management decisions—such as bond refunding, capital investment, and lease versus buy—involve discounting projected future cash flows. What factors must executives consider when choosing a discount rate to apply to forecasted cash flows? ANSWERExplanation / Answer
a)
Year
Cash flow
PV factor 10%
PV
0
$2,000
1.000
$2,000.000
1
$2,000
0.909
$1,818.182
2
$0
0.826
$0.000
3
$1,500
0.751
$1,126.972
4
$2,500
0.683
$1,707.534
5
$4,000
0.621
$2,483.685
$9,136.373
Hence, total present value would be 9,136.37
b)
Year
Cash flow
FV factor 10%
FV
0
$2,000
1.611
$3,221.020
1
$2,000
1.464
$2,928.200
2
$0
1.331
$0.000
3
$1,500
1.210
$1,815.000
4
$2,500
1.100
$2,750.000
5
$4,000
1.000
$4,000.000
$14,714.220
Hence, total future value would be 14,71422
c) We need to calculate PV of all other cash flows:
Year
Cash flow
PV factor 10%
PV
1
$2,000
0.909
$1,818.182
2
$0
0.826
$0.000
3
$1,500
0.751
$1,126.972
4
$2,500
0.683
$1,707.534
5
$4,000
0.621
$2,483.685
$7,136.373
Cash flow required in year 0 = 20,000 -7136.37
= 12,863.63
We need to calculate FV of all other cash flows:
Year
Cash flow
FV factor 10%
FV
0
$2,000
1.611
$3,221.020
1
$2,000
1.464
$2,928.200
2
$0
1.331
$0.000
3
$1,500
1.210
$1,815.000
4
$2,500
1.100
$2,750.000
$10,714.220
Cash flow required in year 5 =( 20,000 -10,7142.22)
= 9,285.78
c) Factors to be considered while choosing discount rate:
1. Risk of the project
2. Cost of sources of capital
3. Capital structure of the firm
Year
Cash flow
PV factor 10%
PV
0
$2,000
1.000
$2,000.000
1
$2,000
0.909
$1,818.182
2
$0
0.826
$0.000
3
$1,500
0.751
$1,126.972
4
$2,500
0.683
$1,707.534
5
$4,000
0.621
$2,483.685
$9,136.373
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