ACCOUNTING-Calculate the present value of the following cash flows

ACC 206
Week Five Problems
Please complete the
following 5 exercises below in either Excel or a word document (but must be
single document). You must show your work where appropriate (leaving the
calculations within Excel cells is acceptable). Save the document, and submit
it in the appropriate week using the Assignment Submission button.
1. Basic present value calculations
Calculate the present value of the following
cash flows, rounding to the nearest dollar:
a.
A single cash inflow of
$12,000 in five years, discounted at a 12% rate of return.
1/(1 + i)^n * f
i = interest rate per period
= rate of return / 4 = 12% / 4
i = 3%
n = number of periods = years * 4 (every 3 months) = 5 * 4
n = 20
f = future payment
f = $12,000
1/(1+.03)^20 = 0.55367575418
(Appendix D shows 0.554)
0.554 * $12,000 =
$6,648 Present Value
b.
An annual receipt of
$16,000 over the next 12 years, discounted at a 14% rate of return.
1/(1 + i)^n * f
i = 14%/4 = 3.5%
n = 12 * 4 = 48
f = $16,000
1/(1+.035)^48 =
0.19180645112
0.192 * $16,000 = $3,072 Present Value
c.
A single receipt of $15,000
at the end of Year 1 followed by a single receipt of $10,000 at the end of Year
3. The company has a 10% rate of return.
1/(1 + i)^n * f
(1/(1+(0.10/4))^(1*4))
* $15,000 = $13,589.25 ≈ $13,589
(1/(1+(0.10/4))^(3*4))
* $10,000 = $7,435.55 ≈ $7,436
$13,589 + $7,436 = $21,025 Present value

d.
An annual receipt of
$8,000 for three years followed by a single receipt of $10,000 at the end of
Year 4. The company has a 16% rate of return.
1/(1 + i)^n * f
(1/(1+(0.16/4))^(3*4))
* $8,000 = $4,996.7764 ≈ $4,997
(1/(1+(0.16/4))^(4*4)))
* $10,000 = $5,339.08176 ≈ $5,339
$4,997 + $5,339 = $10,336 Present Value
2. Cash flow calculationsand net present value
On January 2, 20X1, Bruce Greene invested $10,000 in the
stock market and purchased 500 shares of Heartland Development, Inc. Heartland
paid cash dividends of $2.60 per share in 20X1 and 20X2; the dividend was
raised to $3.10 per share in 20X3. On December 31, 20X3, Greene sold his
holdings and generated proceeds of $13,000. Greene uses the net-present- value
method and desires a 16% return on investments.
a. Prepare a chronological list of the
investment’s cash flows. Note: Greene is entitled to the 20X3 dividend.

Cash outflow

Cash inflow

Net cash flow

Present value factor @ 16%

Present value of net annual cashflow

Initial Cash Outlay – Purchased 500
shares of Heartland Development, Inc.

$10,000

-$10,000
****

1*****

-$10,000

End of Year 20X1

1300*

$1,300

0.862******

$1,121*******

End of Year 20X2

1300**

$1,300

0.743

$966

End of Year 20X3

14550***

$14,550

0.641

$9,327

Net Present
Value =

$1,413

Calculations
* 20X1
Dividends = 500*$2.6
** 20X2
Dividends = 500*$2.6
*** 20X3
Dividends + 20X3 Holdings = (500*$3.10)+$13,000
**** Initial Present
value = 1 (period 0)
****** Appendix C,
Period 1, Rate 16%. Alternatively, = 1/(1 + i)^n = 1/(1+0.16)^1
******* Present Value
* Net Cash Flow = 0.862*$1,300
b. Compute
the investment’s net present value, rounding calculations to the nearest dollar.

Net Present Value =
$1,413
Calculations
= SUM (Present value of net annual cash flow)
= ($10,000) + 1,121 + 966 + 9,327 = $1,413
c. Given
the results of part (b), should Greene have acquired the Heartland stock?
Briefly explain.

The results show that the discounted cash flows produce a
positive net present value of $1,413, suggesting that the shares will return
over 14 percent in excess of the cost of capital. Assuming that 16 percent was
the minimum desired ROI, then they should not have acquired the Heartland stock
since it failed to meet that goal.

3. Straightforwardnet present value and internal rate of return
The City of Bedford is studying a 600-acre site
on Route 356 for a new landfill. The startup cost has been calculated as
follows:
Purchase cost: $450 per acre
Site preparation: $175,000

The site can be used for 20 years before it reaches
capacity. Bedford, which shares a facility in Bath Township with other
municipalities, estimates that the new location will save $40,000 in annual
operating costs.
a. Should
the landfill be acquired if Bedford desires an 8% return on its investment? Use
the net-present-value method to determine your answer.
The net present value is negative $52,280, indicating that
the investment returns less than the 8% cost of capital.

Calculations:
Periods = 20
Desired ROI = 8%
Present Value Factor for $40,000 = 9.818 (Appendix D: 20
Periods, 8%)
Investment Outflows = Purchase Cost + Site Preparation
= $175,000 + ($450*600) = $445,000
Present value of inflows = $40,000 * 9.818 = $392,720
Net Present Value = $392,720 – $445,000 = -$52,280

4. Straightforward net-present-value and payback
computations
STL Entertainment is considering the acquisition
of a sight-seeing boat for summer tours along the Mississippi River. The
following information is available:

Cost of boat

$500,000

Service life

10 summer seasons

Disposal value at the end of 10
seasons

$100,000

Capacity per trip

300 passengers

Fixed operating costs per season
(including straight-line depreciation)

$160,000

Variable operating costs per
trip

$1,000

Ticket price

$5 per passenger

All operating costs, except depreciation, require cash
outlays. On the basis of similar operations in other parts of the country,
management anticipates that each trip will be sold out and that 120,000
passengers will be carried each season. Ignore income taxes.

Instructions:
By using the net-present-value method, determine
whether STL Entertainment should acquire the boat. Assume a 14% desired return
on all investments- round calculations to the nearest dollar.

STL Entertainment should not acquire the boat. The net
present value is negative $264,320, indicating that the investment returns less
than the 14% cost of capital.

Calculations

Cash outflow

Cash inflow

Net cash flow

Present value factor @ 14%

Present value of net annual cashflow

Initial
Cash Outlay – Purchased Boat

$500,000

-$500,000

1

-500,000

End of Year
1

560,000 *

600000 **

$40,000 ***

0.877 ****

35,080
*****

End of Year
2

560,000

600000

$40,000

0.769

30,760

End of Year
3

560,000

600000

$40,000

0.675

27,000

End of Year
4

560,000

600000

$40,000

0.592

23,680

End of Year
5

560,000

600000

$40,000

0.519

20,760

End of Year
6

560,000

600000

$40,000

0.456

18,240

End of Year
7

560,000

600000

$40,000

0.4

16,000

End of Year
8

560,000

600000

$40,000

0.351

14,040

End of Year
9

560,000

600000

$40,000

0.308

12,320

End of Year
10

560,000

700000

$140,000

0.27

37,800

-264,320

* Trips =
120,000 / 300 = 400 trips
Variable operating costs = 400 *
$1000 = $400,000
Fixed Operating Costs = $160,000

** Passengers
per season * Ticket Price
= 120000 * $5

*** Cash inflow
– Cash outflow
= $600,000 – $560,000

**** Appendix C:
Period 1, 14%

***** Present value
factor * Net cash flow
= 0.877 * $40,000

5. Equipment replacement decision
Columbia Enterprises is studying the replacement of some
equipment that originally cost $74,000. The equipment is expected to provide
six more years of service if $8,700 of major repairs are performed in two
years. Annual cash operating costs total $27,200. Columbia can sell the
equipment now for $36,000; the estimated residual value in six years is $5,000.
New equipment is available that will reduce annual cash
operating costs to $21,000. The equipment costs $103,000, has a service life of
six years, and has an estimated residual value of $13,000. Company sales will
total $430,000 per year with either the existing or the new equipment. Columbia
has a minimum desired return of 12% and depreciates all equipment by the
straight-line method.
Instructions:
a. By using the net-present-value method,
determine whether Columbia should keep its present equipment or acquire the new
equipment. Round all calculations to the nearest dollar, and ignore income
taxes.
Columbia should keep its present equipment, which has a net
present value of $1,651,915. This decision is a favorable by $30,516, since
investing in new equipment has a net present value of $1,621,399.

Computations:
First off, $74,000 original cost is a sunken cost.
Therefore, it does not factor into this decision.

Option 1 Cashflows: Repair original
equipment

Cash
outflow

Cash
inflow

Net
cash flow

Present
value factor @ 12%

Present
value of net annual cashflow

End
of Year 1

27,200
*

430,000
***

$402,800****

0.893
*****

359,700
******

End
of Year 2

35,900
**

430,000

$394,100

0.797

314,098

End
of Year 3

27,200

430,000

$402,800

0.712

286,794

End
of Year 4

27,200

430,000

$402,800

0.636

256,181

End
of Year 5

27,200

430,000

$402,800

0.567

228,388

End
of Year 6

27,200

435,000

$407,800

0.507

206,755

Totals

$171,900

$2,585,000

$2,413,100

Net Present Value = 1,651,915 *******

* Annual
Operating Costs
** Annual
Operating Costs + Major Repairs
= $27,200 + $8,700
*** Company
Sales
**** Cash inflow
– Cash outflow
= 403,000 – 27,200
***** Appendix C,
Period 1, 12%
****** Present
Value factor * Net Cash Flow = .893 * $402,800
******* SUM(Present
value of net annual cashflow) = 359,700 + 314,098 + 286,794 + 256,181 + 228,388
+ 206,755

Option 2 Cashflows: Invest in new equipment

Cash
outflow

Cash
inflow

Net
cash flow

Present
value factor @ 12%

Present
value of net annual cashflow

Initial
Cash Outlay – Sell old equipment and purchase new equipment

$103,000
*

36000
***

-$67,000

1

-67,000

End
of Year 1

21,000
**

430,000
****

$409,000
****

0.893
*****

365,237

End
of Year 2

21,000

430,000

$409,000

0.797

325,973

End
of Year 3

21,000

430,000

$409,000

0.712

291,208

End
of Year 4

21,000

430,000

$409,000

0.636

260,124

End
of Year 5

21,000

430,000

$409,000

0.567

231,903

End
of Year 6

21,000

443,000

$422,000

0.507

213,954

Totals

$229,000

$2629000

$2,400,000

Net
present value = $1,621,399

* Purchase
new equipment
** Annual
Operating Costs
*** Sell
original equipment
**** Cash inflow
– Cash outflow
=
409,000 – 430,000
***** Appendix C,
Period 1, 12%
****** Present
Value factor * Net Cash Flow = .893 * $402,800
******* SUM(Present
value of net annual cashflow)
=
-67,000 + 365,237 + 325,973 + 291,208 + 260,124 + 231,903 + 213,954
b. Columbia’s
management feels that the time value of money should be considered in all
long-term decisions. Briefly discuss the rationale that underlies management’s
belief.

If you only factored in net cash flow over 6 years, this
appears to be a closer decision. Option 1 yields a net cash flow of $2,413,100,
compared to Option 2’s cash flow of $2,400,000, a difference of a mere $13,100.
Yet the net present-value difference is
$30,516. So why is this a greater difference? This leads to the concept
of Time value of money.

Here’s a scenario that illustrates that the value of money
is relative to time. Why would you receive a discount for paying auto insurance
for an entire six months up front, vs. sticking with the monthly rate? While we
have an intuitive understanding that money upfront is more valuable than money
promised to be paid in the future, Capital Budgeting Analysis seeks to use
industry-standard methodologies to calculate exactly just how much more it is
worth. This includes Future Value, which is rather intuitive: it’s what an
investment will be worth in the future. This leads to Present value, which is
opposite of Future Value. I never would have figured that out and it’s really
fascinating to see how mathematical formulas correspond to the linguistics of
logical decision making.

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