Question

Name 4) Fill in the following table to caloulate the net present vallue and benefit/cost ratio of each investment. Round to the nearest dollar or hundredth in the benefit/cost ratio. Investment B Investment A Yearly After-tax Yearly Present After-tax Present After-tax After-tax Present Value Year Value Present Value Year Value x of Benefits of Benefits Benefit Benefit Factor Factor 3200 1850 2 1925 2 3200 2567 3200 3 4 3850 3000 3000 3850 Total 6 5133 Less Initial Cost 7 5775 Net Present Value 8 5850 Benefit/Cost Ratio Total 30,800 I Less Initial Cost Net Present Value Benefit/Cost Ratio 5) If TOM's Tomatoes and Herbs, LLC can only afford to invest in one project, which project should they invest in and why? 6) What is the Equivalent Annual Cost of each investment to TOM's Tomatoes and Herbs, LLC? Investment A Investment B

Answer 1

Investment A
Year	cost	Cash flow	working	cost yet to be recovered
0	16000	0		-
1		1,850	16000-1850	14,150
2		1,925	14150-1925	12,225
3		2,567	12225-2567	9,658
4		3,850	9658-3850	5,808
5		3,850	5808-3850	1,958
6		5,133	1958-5133	-3,175
7		5,775
8		5,850

as we can see that the cost to be recovered turns negative in the 6th year

that means that the cost is recovered between 5th and 6th year

Now, Payback period = years before full recovery + (Unrecovered investment at start of the year/Cash flow during the year)

Payback period =5 + (1958/5133)

Payback period =5.38 years or 5 years 4.5 months

So payback period of Investment A is 5 years aprox.

investment B
Year	cost	Cash flow	working	cost yet to be recovered
0	9500	0		-
1		3,200	9500-3200	6,300
2		3,200	6300-3200	3,100
3		3,200	3100-3200	-100
4		3,000
5		3,000

as we can see that the cost to be recovered turns negative in the 3rd year

that means that the cost is recovered between 2nd and 3rd year

Now, Payback period = years before full recovery + (Unrecovered investment at start of the year/Cash flow during the year)

Payback period =2 + (3100/3200)

Payback period =2.97 years or 2 years 11.6 months or 3 years approx.

So payback period of Investment b is 3 years

2. As we can see that investment A takes 5 years to payback the initial cost and investment B takes 3 years to payback the initial cost,

We will choose investment B , as it takes less time to payback the cost and so is more profitable.

Investment	years								Average
A	1	2	3	4	5	6	7	8
after tax benefit	1,850	1,925	2,567	3,850	3,850	5,133	5,775	5,850
value of A
1st Jan	-	1,850	3,775	6,342	10,192	14,042	19,175	24,950
31st Dec	1,850	1,925	2,567	3,850	3,850	5,133	5,775	5,850
Average	1850	1887.5	2114	2548	2,808.40	3,195.83	3,564.29	3850
	Average annual rate of return for A								26%

Here , 1^st jan balance is last years closing balance

Closing balance is the after tax benefit of that years

Average is the opening balance + closing balance / number of years

For example. For the 2^nd year

Opening balance = 1850

Closing = 1925

Average = 1850+1925/2

Average annual rate of return = average annual net earning / initial cost *100

Here annual avg earning= 3850

Initial cost = investment –salvage value

= 16000-1000

AARR= 3850/(16000-1000) *100

= 25.67 or 26%

Similarly for investment B

investment	years								Average
B	1	2	3	4	5
after tax benefit	3200	3200	3200	3000	3000
value of B
1st Jan	-	3,200	6,400	9,600	12,600
31st Dec	3,200	3,200	3,200	3,000	3,000
Average	3200	3200	3200	3150	3,120.00
	Average annual rate of return for B								35%

4. Investment A

Year (n)	Cash Flow	working : factor= 1/(1+r)^n (r= 8.00%)	present value factor = 1/(1+r)^n	after tax present value = Cash flow * discount value
1	1,850	1/ (1+0.08)^1	0.93	$                     1,712.96
2	1,925	1/ (1+0.08)^2	0.86	$                     1,650.38
3	2,567	1/ (1+0.08)^3	0.79	$                     2,037.77
4	3,850	1/ (1+0.08)^4	0.74	$                     2,829.86
5	3,850	1/ (1+0.08)^5	0.68	$                     2,620.25
6	5,133	1/ (1+0.08)^6	0.63	$                     3,234.66
7	5,775	1/ (1+0.08)^7	0.58	$                     3,369.66
8	5,850	1/ (1+0.08)^8	0.54	$                     3,160.57
			Total	$                   20,616.11
			Less : initial investment	$                   16,000.00
			Net present value	$                     4,616.11
			benefit cost ratio	= 20616/16000= 1.29

Investment B

Year (n)	Cash Flow	working : factor= 1/(1+r)^n (r= 8.00%)	present value factor = 1/(1+r)^n	after tax present value = Cash flow * discount value
1	3,200	1/ (1+0.08)^1	0.93	$                     2,962.96
2	3,200	1/ (1+0.08)^2	0.86	$                     2,743.48
3	3,200	1/ (1+0.08)^3	0.79	$                     2,540.26
4	3,000	1/ (1+0.08)^4	0.74	$                     2,205.09
5	3,000	1/ (1+0.08)^5	0.68	$                     2,041.75
			Total	$                   12,493.55
			Less : initial investment	$                     9,500.00
			Net present value	$                     2,993.55
			benefit cost ratio	1.32