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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