Problem 26-3A (Part Level Submission) Brooks Clinic is considering investing in
ID: 2584487 • Letter: P
Question
Problem 26-3A (Part Level Submission) Brooks Clinic is considering investing in new heart-monitoring equipment. It has two options. Option A would have an initial lower cost but would require a significant expenditure for rebuilding after 4 years. Option B would require no rebuilding expenditure, but its maintenance costs would be higher. Since the Option B machine is of initial higher quality, it is expected to have a salvage value at the end of its useful life. The following estimates were made of the cash flows. The company’s cost of capital is 6%. Option A Option B Initial cost $186,000 $277,000 Annual cash inflows $72,200 $82,700 Annual cash outflows $28,000 $26,800 Cost to rebuild (end of year 4) $51,000 $0 Salvage value $0 $8,600 Estimated useful life 7 years 7 years Click here to view PV table. (a) Compute the (1) net present value, (2) profitability index, and (3) internal rate of return for each option. (Hint: To solve for internal rate of return, experiment with alternative discount rates to arrive at a net present value of zero.)
Explanation / Answer
Solution:
Part 1 – Calculation of Net Present Value
Net Present Value is the difference of Present Value of all future expected cash flows and Present Value of Initial Investment.
Annual Cash Flow for Option A = Annual Cash Inflow – Annual Cash Outflow = 72200 – 28,000 = $44,200
Annual Cash Flow for Option B = 82,700 – 26,800 = 55,900
Net Present Value
Option A
Option B
Year
Cash Flow
PV factor @ 6%
Present Value of Cash Flow
Cash Flow
Present Value of Cash Flow
(A)
(B)
(A*B)
(X)
(X*B)
1
Annual Cash Flow
$44,200
0.943
$41,698
$55,900
$52,736
2
Annual Cash Flow
$44,200
0.890
$39,338
$55,900
$49,751
3
Annual Cash Flow
$44,200
0.840
$37,111
$55,900
$46,935
4
Annual Cash Flow - Cost to rebuild for option B
$44,200
0.792
$35,011
$4,900
(55900-51000)
$3,881
5
Annual Cash Flow
$44,200
0.747
$33,029
$55,900
$41,772
6
Annual Cash Flow
$44,200
0.705
$31,159
$55,900
$39,407
7
Annual Cash Flow + Salvage Value
$44,200
0.665
$29,396
$64,500
(55900+8600)
$42,896
Present Value of Cash Flows
$246,741
$277,378
Less: Present Value of Initial Investment (Cash Outflow)
($186,000)
($277,000)
Net Present Value
$60,741
$378
Part 2 -- Profitability Index
Profitability Index = Present Value of Cash Inflows / Present Value of Cash Outflows
Option A
Option B
Profitability Index
Present Value of Cash Inflows (X)
$246,741
$277,378
Present Value of Initial Investment or Cash Outflows (Y)
$186,000
$277,000
Profitability Index (X/Y)
1.327
1.001
Part 3 -- Internal Rate of Return (IRR)
By using following steps we can calculate IRR:
Step-I: We estimate Initial Rate of discounting and NPV is calculated by using that rate
Step-II
- If 1st NPV is Positive increase the discounting rate
- If NPV is Negative decrease the discounting rate
Step-III: Apply this formula
IRR =
Lower Rate +
Net Present Value at Lower Rate
Diff. in NPV at Lower & Higher Rate
X Diff. in Rate
For Option A
Option A
Year
Cash Flow
PV factor @ 15%
Present Value of Cash Flow
PV factor @ 14.5%
Present Value of Cash Flow
(A)
(B)
(A*B)
(Z)
(A*Z)
1
Annual Cash Flow
$44,200
0.870
$38,435
0.873
$38,603
2
Annual Cash Flow
$44,200
0.756
$33,422
0.763
$33,714
3
Annual Cash Flow
$44,200
0.658
$29,062
0.666
$29,445
4
Annual Cash Flow - Cost to rebuild for option B
$44,200
0.572
$25,271
0.582
$25,716
5
Annual Cash Flow
$44,200
0.497
$21,975
0.508
$22,459
6
Annual Cash Flow
$44,200
0.432
$19,109
0.444
$19,615
7
Annual Cash Flow + Salvage Value
$44,200
0.376
$16,616
0.388
$17,131
Present Value of Cash Flows
$183,891
$186,682
Less: Present Value of Initial Investment (Cash Outflow)
($186,000)
($186,000)
Net Present Value
($2,109)
$682
IRR for Option A =
IRR =
Lower Rate +
Net Present Value at Lower Rate
Diff. in NPV at Lower & Higher Rate
X Diff. in Rate
= 14.5 + $682 / ($682 – (-2,109)) x (15 - 14.5)
= 14.5 + 682 / 2792 x 0.5
= 14.5 + 0.24x0.5
= 14.5% + 0.12
= 14.62%
IRR for Option B
NPV at 6% = $378
Calculation of NPV at 7%
Year
Cash Flow
PV factor @ 6.2%
Present Value of Cash Flow
(X)
(Y)
(X*Y)
1
Annual Cash Flow
$55,900
0.942
$52,637
2
Annual Cash Flow
$55,900
0.887
$49,564
3
Annual Cash Flow
$55,900
0.835
$46,670
4
Annual Cash Flow - Cost to rebuild for option B
$4,900
0.786
$3,852
5
Annual Cash Flow
$55,900
0.740
$41,380
6
Annual Cash Flow
$55,900
0.697
$38,964
7
Annual Cash Flow + Salvage Value
$64,500
0.656
$42,334
Present Value of Cash Flows
$275,400
Less: Present Value of Initial Investment (Cash Outflow)
($277,000)
Net Present Value
($1,600)
IRR =
Lower Rate +
Net Present Value at Lower Rate
Diff. in NPV at Lower & Higher Rate
X Diff. in Rate
= 6 + $378 / (378 – (-1600) x (6.2 - 6)
= 6 + 378 / 1978 x 0.2
= 6 + 0.19 x 0.2
= 6 + 0.038
= 6.038%
Hope the above calculations, working and explanations are clear to you and help you in understanding the concept of question.... please rate my answer...in case any doubt, post a comment and I will try to resolve the doubt ASAP…thank you
Option A
Option B
Year
Cash Flow
PV factor @ 6%
Present Value of Cash Flow
Cash Flow
Present Value of Cash Flow
(A)
(B)
(A*B)
(X)
(X*B)
1
Annual Cash Flow
$44,200
0.943
$41,698
$55,900
$52,736
2
Annual Cash Flow
$44,200
0.890
$39,338
$55,900
$49,751
3
Annual Cash Flow
$44,200
0.840
$37,111
$55,900
$46,935
4
Annual Cash Flow - Cost to rebuild for option B
$44,200
0.792
$35,011
$4,900
(55900-51000)
$3,881
5
Annual Cash Flow
$44,200
0.747
$33,029
$55,900
$41,772
6
Annual Cash Flow
$44,200
0.705
$31,159
$55,900
$39,407
7
Annual Cash Flow + Salvage Value
$44,200
0.665
$29,396
$64,500
(55900+8600)
$42,896
Present Value of Cash Flows
$246,741
$277,378
Less: Present Value of Initial Investment (Cash Outflow)
($186,000)
($277,000)
Net Present Value
$60,741
$378
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.