The following information is available to use in deciding whether to purchase the new backhoes or old backhoes. Using the 8% Present Value of an Annuity of 1 Old Backhoes New Backhoes Purchase cost when new $90,000 $200,000 Salvage value now $42,000 Investment in major overhaul needed in next year $55,000 Salvage value in 8 years $15,000 $90,000 Remaining life 8 years 8 years Net cash flow generated each year $30,425 $43,900
My Questions is: Can you display what the pay back period is for the New and Old backhoes from using the calculations from the chart you answered.
- The following information is available to use in deciding whether to purchase the new backhoes or old backhoes. Using the 8% Present Value of an Annuity of 1
|
Old Backhoes |
New Backhoes |
||
|
Purchase cost when new |
$90,000 |
$200,000 |
|
|
Salvage value now |
$42,000 |
||
|
Investment in major overhaul needed in next year |
$55,000 |
||
|
Salvage value in 8 years |
$15,000 |
$90,000 |
|
|
Remaining life |
8 years |
8 years |
|
|
Net cash flow generated each year |
$30,425 |
$43,900 |
Answer that Bartebly provided is down below.
Hello the Profitability index was answered already so can you provide the pay back period for New and Old Backhoes. Thank you
My Questions is: Can you display what the pay back period is for the New and Old backhoes from using the calculations from the chart you answered.
Expert Answer
Meaning of
Net present value(NPV) is the difference between the PV of cash inflows and the PV of cash outflows over a period of time. It is used in capital budgeting and investment planning to analyze the profitability of a project.
How to Find PV factor using Calculator:-
To Find PV factor following Steps are followed :- (We are using 8% as given in Question above we need to find Present Value)
1) To Find PV of any number using Calculator type that number Calculator (say 8 )
2) Divide that number (Say 8 ) by 100 ,so the result is 0.08
3) Add 1 to the above number, So the result is 1.08
4) So the factor of 8% is 1.08 , similarly the factor of 5% is 1.05, factor of 10% is 1.10, factor of 12% is 1.12, factor of 23% is 1.23.
5) Now Type the Factor of 8% that is 1.08 on Calculator and Press Divided and then equal to , the result is .926 (rounded off) , it means $1 (after 1year ) has the present value of $0.926 . IF $1 Present Value is 0.926 , then $30425 PV will be $30425* 0.926 = $ 28174 (rounded off)
6) Press equal to again, the result is 0.857 (rounded off) it means $1 (after 2year ) has the present value of $0.857. IF $1 Present Value is 0.857 , then $30425 PV will be $30425* 0.857 = $ 26074 (rounded off).
Meaning of Profitability Index :-
Profitability Index is a capital budgeting tool used to rank projects on the basis of their profitability. It is calculated by dividing the present value of all cash inflows by the initial investment. Projects with higher profitability index are better.
Formula for Profitability Index :-
| Profitability Index = | P.V of |
| Initial Investment |
Since NPV equals the PV cash inflows minus PV of Cash Outflows, we can write the present value of future value as the sum of net present value and initial investment:
| Profitability Index = | Initial Investment + NPV |
| Initial Investment |
= 1 + (NPV/ Initial Investment)
Old Backhoes
Present Value of
| Year | Cash Inflows | PV Factor @8% | Present Value |
| 1 | 30425 | 0.926 | 28174 |
| 2 | 30425 | 0.857 | 26074 |
| 3 | 30425 | 0.794 | 24157 |
| 4 | 30425 | 0.735 | 22362 |
| 5 | 30425 | 0.681 | 20719 |
| 6 | 30425 | 0.63 | 19168 |
| 7 | 30425 | 0.583 | 17738 |
| 8 | 30425 | 0.54 | 16430 |
| 8 | 15000 | 0.54 | 8100 |
P.V of Cash Inflow (Total) 182922
In 8th year we will also receive salvage Value of $15000.
|
Year |
Amount (col2) |
PV factor of 8% (col3) |
Present Value(col2*col3) |
|
0 |
90,000 |
1 |
90,000 |
|
1 |
55,000 |
1/1.08 =.926 |
50,930 |
|
|
|
PV OF |
140,930 |
Therefore, NPV = 182,922 - 140,930 = 41,992.
Initial Investment = 90,000
Therefore Profitability Index = 1+ 41992/90000 = 1.47 ( rounded off)
New Backhoes
Initial Investment = $ 200,000
PV of Cash Inflow
|
Year |
Inflow Amount (col2) |
PV factor of 8% (col3) |
Present Value(col2*col3) |
|
1 |
43,900 |
1/1.08 = 0.926 |
40651 |
|
2 |
43,900 |
1/(1.08)2 = 0.857 |
37622 |
|
3 |
43,900 |
1/(1.08)3 = 0.794 |
34857 |
|
4 |
43,900 |
0.735 |
32267 |
|
5 |
43,900 |
0.681 |
29896 |
|
6 |
43,900 |
0.630 |
27657 |
|
7 |
43,900 |
0.583 |
25594 |
|
8 |
43,900 |
0.540 |
23706 |
|
9 |
90,000 (Salvage Value) |
0.540 |
48600 |
|
|
|
PV OF INFLOW |
300,850 |
In 8th year we will also receive salvage Value of $90,000.
NPV = 300,850 - 200,000 = 100,850
Therefore Profitability Index = 1+ 100850/200000 = 1.50 ( rounded off)
Conclusion :- Since the Profitability Index of New Backhoes is higher than that of Old Backhoes ..It is better to go with New Backhoes.
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