Maple Products is considering the introduction of a new product with the estimat
ID: 2654509 • Letter: M
Question
Maple Products is considering the introduction of a new product with the estimated cash flows shown below. Evaluate the following Cash Flows using the criteria in parts a-d with a MARR of 20%. Indicate for each evaluation whether the proposal should be accepted or rejected. Show excel calculations/formula's. Year 0 1 2 3 4 5 Cash Flow ($250,000) $50,000 $100,000 $150,000 $150,000 $150,000 a Present Worth (PW) b Annual Worth (AW) c Internal rate of Return (IRR) d Discounted Payback by end of year (EOY) 3 Maple Products is considering the introduction of a new product with the estimated cash flows shown below. Evaluate the following Cash Flows using the criteria in parts a-d with a MARR of 20%. Indicate for each evaluation whether the proposal should be accepted or rejected. Show excel calculations/formula's. Year 0 1 2 3 4 5 Cash Flow ($250,000) $50,000 $100,000 $150,000 $150,000 $150,000 a Present Worth (PW) b Annual Worth (AW) c Internal rate of Return (IRR) d Discounted Payback by end of year (EOY) 3Explanation / Answer
(‘a) Present Worth ( PW)= Present Value of Cash Inflows – Initial Investment
Year (n)
Cash Flows ($)
Discounting Factor
@ 20 % ( 1.20)-n
Present Value ($)
0
(250,000)
1.00
(250,000)
1
50,000
0.833
41,666.67
2
100,000
0.694
69,444.44
3
150,000
0.579
86,805.56
4
150,000
0.482
72,337.96
5
150,000
0.402
60,281.64
Total
80,536
PW (20 %)= (CF1 x (1+r)-1 + CF2 x (1+r)-2 + CF3 x (1+r)-3 + CF4 x (1+r)-4 + CF5 x (1+r)-5 ] – CF0
PW (20 %)= $ 80,536
(‘c ) Internal Rate of Return
Year (n)
Cash Flows ($)
Discounting Factor
@ 31 % ( 1.31)-n
PW (31 %)($)
DF @ 32 %
PW (32 %)
(1+r)-n
0
(250,000)
1.00
(250,000)
1.00
(250,000)
1
50,000
0.763
38,167.94
0.758
37,878.79
2
100,000
0.583
58,271.66
0.574
57,392.10
3
150,000
0.445
66,723.28
0.435
65,218.30
4
150,000
0.340
50,933.80
0.329
49,407.80
5
150,000
0.259
38,880.76
0.250
37,430.15
Total
2,977
(2,673)
PW ( 31 %)= $ 2977
PW ( 32 %) = $(2,673)
IRR is the rate at which PW is zero
It means PW (IRR)= 0
When rate increase by 1 % , PW decrease by $ 5,650 ( 2977 + 2673)
So for a reduction of $ 2977 in PW, increase in rate required
Increase in rate = (2977 x 1 )/ 5650= 0.53 %
Hence IRR = 31 % + 0.53 %
IRR= 31.53 %
(d) Discounted Payback by the end of year 3
Year (n)
Cash Flows ($)
Discounting Factor
@ 20 % ( 1.20)-n
Discounted Cash Flow
Cumulative Discounted cash Flow
1
50,000
0.833
41,666.67
41,666.67
2
100,000
0.694
69,444.44
111,111.11
3
150,000
0.579
86,805.56
197,916.67
4
150,000
0.482
72,337.96
270,254.63
5
150,000
0.402
60,281.64
330,536.27
Total
80,536
Discounted Payback = Discounted payback how much initial investment is returned back by the project at the end of a particular period.
In this given case discounted payback at the end of year 3 = $ 197,917. It means out of investment made of $ 250,000 $ 197,917 has been recovered at the end of year 3 .
The project has returned all initial investment in the 4th year, because at the end of year 4, total cash flow generated exceeds the initial investment.
(‘b) Annual Worth
Year
Cash Flow
Factor
Annual Worth ($)
0
(250,000)
0.3344
-83,600
1
50,000
1.00
50,000
2
100,000
0.4545
45,450
3
150,000
0.2747
41,205
4
150,000
0.1863
27,945
5
150,000
0.1344
20,160
Total
101,160
AW (20%) = -250,000 x (A/P, 20 %, 5) + 50,000 x (A?F, 20 %,1) + 100000 x (A/F, 20%,2 ) + 150,000 x (A/F , 20 %, 3) + 150,000 x (A/F, 20 % ,4 ) + 150,000 x (A/F, 20 %, 5)
AW (20%)= $ 101,160
Formula (A/P, ‘i % , n ) = ‘ix (1+’i)n / (1+i)n -1
Formula ( A/F, i%, n) = ‘i/ (1+i)n -1
Conclusion –
As IRR is greater than MARR
PW is positive
AW is positive
All initial investment is recovered in the year 4 ,
Hence project should be accepted
Year (n)
Cash Flows ($)
Discounting Factor
@ 20 % ( 1.20)-n
Present Value ($)
0
(250,000)
1.00
(250,000)
1
50,000
0.833
41,666.67
2
100,000
0.694
69,444.44
3
150,000
0.579
86,805.56
4
150,000
0.482
72,337.96
5
150,000
0.402
60,281.64
Total
80,536