## Solution Manual for Stice IA,18Edition 2012

Fair Value Module

An Excel spreadsheet that contains the details of the calculations for the Fair Value

Module solutions is available on the IRCD and instructor Web site.

EXERCISES

FV–1. Building 3

• Look at the 7% capitalization rate row.

• Based on square footage, Building 3 is 80% of the way from

$2,000,000 to $2,500,000.

• Estimated fair value of Building 3 = $2,400,000 = $2,000,000 +

0.8($2,500,000 – $2,000,000)

Building 4

• Look at the 8% capitalization rate row.

• Based on square footage, Building 4 is 10% of the way from

$2,250,000 to $2,625,000.

• Estimated fair value of Building 4 = $2,287,500 = $2,250,000 +

0.1($2,625,000 – $2,250,000)

Building 5

• Look at the 10% capitalization rate row.

• Based on square footage, Building 5 is 60% of the way from

$1,800,000 to $2,100,000.

• Estimated fair value of Building 5 = $1,980,000 = $1,800,000 +

0.6($2,100,000 – $1,800,000)

FV–2. Selling Price

Square Feet

Capitalization Rate 10,000 20,000 30,000 40,000 50,000

7%…………………… $700,000 $1,425,000 $2,000,000 $2,500,000 $3,000,000

8%…………………… 625,000 1,250,000 1,750,000 2,250,000 2,625,000

9%…………………… 550,000 1,100,000 1,550,000 2,000,000 2,300,000

10%…………………… 500,000 1,000,000 1,400,000 1,800,000 2,100,000

9.3%…………………… 535,000 1,070,000 1,505,000 1,940,000 2,240,000

Building Z

• Look at the 9.3% capitalization rate row which was created by

interpolation between the 9% and 10% rows.

• Based on square footage, Building Z is 20% of the way from

$1,505,000 to $1,940,000.

• Estimated fair value of Building Z = $1,592,000= $1,505,000 +

0.2($1,940,000 – $1,505,000)

FV-2 Fair Value Module

FV–3.

• Look at the AA bond rating column.

• Based on the term of the bond, the bond is 30% of the way from 100 to

91.

• 100 – (0.3 × 9) = 97.3

• Estimated fair value of the bond = 0.973 × $1,000 = $973

FV–4. Bond 3

• Look at the AAA bond rating column.

• Based on the term of the bond, Bond 3 is one-third of the way from

103.85 to 103.66.

• Estimated bond price as a percent of par = 103.787 = 103.85 –

1/3(103.85 – 103.66)

• Estimated price of Bond 3 = 1.03787 × $1,000 = $1,037.87

Bond 4

• Look at the BB bond rating column.

• Based on the term of the bond, Bond 4 is 80% of the way from 91.98 to

82.06.

• Estimated bond price as a percent of par = 84.044 = 91.98 – 0.8(91.98 –

82.06)

• Estimated price of Bond 4 = 0.84044 × $1,000 = $840.44

Bond 5

• Look at the A bond rating column.

• Based on the term of the bond, Bond 5 is 80% of the way from 101.45

to 99.56.

• Estimated bond price as a percent of par = 99.938 = 101.45 –

0.8(101.45 – 99.56)

• Estimated price of Bond 5 = 0.99938 × $1,000 = $999.38

FV–5. Customer List

Outcome 1: PMT = $40,000; I = 8%; N = 5 years → $159,708

Outcome 2: PMT = 18,000; I = 8%; N = 4 years → 59,618

Outcome 3: PMT = 9,000; I = 8%; N = 3 years → 23,194

Present Probability-Weighted

Value Probability Present Value

Outcome 1……….. $159,708 0.20 $31,942

Outcome 2……….. 59,618 0.30 17,885

Outcome 3……….. 23,194 0.50 11,597

Total estimated fair value……………………….. $61,424

Fair Value Module FV-3

FV–5. (Concluded)

Franchise Agreement

Outcome 1: PMT = $450,000; I = 8%; N = 10 years → $3,019,537

Outcome 2: PMT = 12,000; I = 8%; N = 4 years → 39,746

Outcome 3: PMT = 500; I = 8%; N = 3 years → 1,289

Present Probability-Weighted

Value Probability Present Value

Outcome 1……….. $3,019,537 0.10 $301,954

Outcome 2……….. 39,746 0.20 7,949

Outcome 3……….. 1,289 0.70 902

Total estimated fair value……………………….. $310,805

FV–6. The fair value of the business license is $42,979, computed as follows:

Discount rate……………………………………………… 15.0%

Royalty rate……………………………………………….. 2.0%

Initial annual cab revenue growth rate………… 10.0%

Terminal growth rate (after five years)………… 3.0%

Income tax rate ………………………………………….. 30%

Growth 3%

Year 1 Year 2 Year 3 Year 4 Year 5 Years 5+

Total annual revenue … $ 300,000 $ 330,000 $ 363,000 $ 399,300 $ 439,230

Pretax royalty (2%)……. $ 6,000 $ 6,600 $ 7,260 $ 7,986 $ 8,785

Income taxes (30%)…… 1,800 1,980 2,178 2,396 2,636

After-tax royalty………… $ 4,200 $ 4,620 $ 5,082 $ 5,590 $ 6,149 $52,779

Discounted cash flow .. $ 3,652 $ 3,493 $ 3,341 $ 3,196 $ 3,057

Sum of discounted cash flow………………….. $ 16,739

Present value of “perpetuity”………………….. 26,240

Total present value of cash flows……………. $ 42,979

FV–7. We can estimate a “depreciated” replacement cost using a process

exactly analogous to the computation of depreciated book value. The

computations are as follows:

• ($800,000 – $40,000) ÷ 16 years = $47,500 “depreciation” per year

• 7 years × $47,500 “depreciation” per year = $332,500 total

“depreciation”

• $800,000 replacement cost new – $332,500 “depreciation” = $467,500

adjusted replacement cost

This $467,500 adjusted replacement cost is a cost-based estimate of the

fair value of the rock crushing system. If it is more reasonable to assume

that the system loses value more quickly in the early years, then an

accelerated depreciation method can be used.

FV-4 Fair Value Module

FV–8. Note: These securities are reported at fair value on a recurring basis.

Fair Value Measurements at Reporting Date Using

Quoted Prices

in Active Significant

Markets for Other Significant

Identical Observable Unobservable

Assets Inputs Inputs

Description Total (Level 1) (Level 2) (Level 3)

Trading securities……………. $27,000 $27,000

Available-for-sale securities 35,340 $29,340 $6,000

Total ……………………………….. $62,340 $27,000 $29,340 $6,000

Fair Value Measurements Using

Significant Unobservable Inputs

(Level 3)

Real Estate

Investment Trust

Security 3

Beginning balance……………………………………………….. $ 5,400

Total gains or losses (realized/unrealized)

Included in earnings ………………………………….. 0

Included in other comprehensive income …… (2,600)

Purchases………………………………………………………. 3,200

Transfers in or out of Level 3…………………………… 0

Ending balance ……………………………………………………. $ 6,000

The unrealized decrease of $2,600 recognized in other comprehensive

income this year is computed as follows:

Beginning of Year Ending of Year

Market Market

Securities Cost Value Cost Value

First purchase…………………………. $ 4,500 $ 5,400 $ 4,500 $ 3,600

Second purchase…………………….. 0 0 3,200 2,400

Total ……………………………………….. $ 4,500 $ 5,400 $ 7,700 $ 6,000

Cumulative unrealized gain or

loss at the beginning of year ($5,400 – $4,500) Unrealized gain $900

Cumulative unrealized gain or

loss at the end of Year 2 ($6,000 – $7,700) Unrealized loss $1,700

To get from a cumulative unrealized gain of $900 to a cumulative

unrealized loss of $1,700 required an UNREALIZED LOSS of $2,600 for

the year.

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