Chapter 6 Given no established value for the building

CHAPTER 6

Accounting and the Time Value of Money

SOLUTIONS TO B PROBLEMS

PROBLEM 6-1B

(a) Given no established value for the building, the fair market value of

the note would be estimated to value the building.

Time diagram:

Formula: PV = FV (PVFn, i)

Cash equivalent price of building …………………………….

$294,012

Less: Book value ($411,000 – $163,000) …………………..

PROBLEM 6-1B (Continued)

(b) Time diagram:

i = 5%

Principal

$1,000,000

Interest

PV – OA = ? $60,000 $60,000 $60,000 $60,000

Present value of the principal

FV (PVF20, 8%) = $1,000,000 (0.21455) ……………..

= $214,550

Present value of the interest payments

R (PVF – OA80, 8%) = $60,000 (9.81815) …………..

Combined present value (purchase price) …………….

(c) Time diagram:

i = 10%

PV – OA = ? $10,000 $10,000 $10,000 $10,000 $10,000

PROBLEM 6-1B (Continued)

(d) Time diagram:

i = 8%

PV – OA = ?

$50,000 $15,000 $15,000 $15,000 $15,000 $15,000

Formula: PV – OA = R (PVF – OAn,i)

PV – OA = $15,000 (PVF – OA5, 8%)

(e) Time diagram:

i = 9%

PV – OA = ? $500,000 $500,000 $500,000 $500,000

Formula: PV – OA = R (PVF – OAn, i)

PROBLEM 6-2B

(a) Time diagram:

i = 6% FV – OA = $220,000

R R R R

R = ? ? ? ?

Formula: FV – OA = R (FVF – OAn,i)

(b) Time diagram:

i = 8%

FV – AD =

R R R R 2,500,000

R = ? ? ? ?

PROBLEM 6-2B (Continued)

1.

Future value of an ordinary annuity of 1 for

38 periods at 8% …………………………………………

220.31595

Factor (1 + 0.08) …………………………………………….

(c) Time diagram:

i = 4%

PV = $60,000 FV = $96,062

0 1 2 3 n

Future value approach

Present value approach

FV = PV (FVFn, i)

PV = FV (PVFn, i)

$96,062 = $60,000 (FVFn, 4%)

PROBLEM 6-2B (Continued)

(d) Time diagram:

i = ?

PV = FV =

$35,367 $41,000

0

1

4 5

n = 5

Future value approach

Present value approach

FV = PV (FVFn, i)

PV = FV (PVFn, i)

$41,000 = $35,367 (FVF5, i)

$35,367= $41,000 (PVF5, i)

= $41,000 ÷ $35,367

= $35,367÷ $41,000

PROBLEM 6-3B

Time diagram (Bid A):

i = 8%

$65,600

PV – OA = R =

? 1,520 1,520 65,600 1,520 1,520 65,600 1,520 1,520 0

Present value of initial cost

8,000 X $8.20 = $65,600 (incurred today) ………………..

$ 65,600

Present value of maintenance cost (years 1–4)

8,000 X $0.19 = $1,520

R (PVF – OA4, 8%) = $1,520 (3.31213) ……………………….

5,034

Present value of resurfacing (year 5)

FV (PVF5, 8%) = $65,600 (0.68058) …………………………...

Present value of maintenance cost (years 6–9)

R (PVF – OA9–5, 8%) = $1,520 (6.24689 – 3.99271) ………

3,426

Present value of resurfacing (Year 10)

FV (PVF10, 8%) = $65,600 (0.46319) …………………………..

Present value of maintenance cost (years 11–14)

R (PVF – OA14–10, 8%) = $1,520 (8.24424 – 6.71008) ……

2,332

Present value of outflows for Bid A ………………………….

$151,423

PROBLEM 6-3B (Continued)

Time diagram (Bid B):

i = 8%

$136,800

PV – OA = R =

? 1,040 1,040 1,040 1,040 1,040 0

0 1 2 3 13 14 15

n = 14

Present value of initial cost

8,000 X $17.10 = $136,800 (incurred today) ………..

$136,800

Present value of maintenance cost

8,000 X $0.13 = $1,040

R (PV – OA14, 8%) = $1,040 (8.24424) ……………………

PROBLEM 6-4B

Lump sum alternative: Present Value = $2,500,000 X (1 – 0.40) = $1,500,000.

PROBLEM 6-5B

(a) The present value of $200,000 cash paid today is $200,000.

(b) Time diagram:

i = 2% per quarter

PV – OA = R =

? $12,000 $12,000 $12,000 $12,000 $12,000

(c) Time diagram:

i = 2% per quarter

$50,000

PV – AD =

R = $5,000 $5,000 $5,000 $5,000 $5,000 0

PROBLEM 6-5B (Continued)

(d) Time diagram:

i = 2% per quarter

PV – OA = R =

? $3,750 $3,750 $3,750 $3,750

PV – OA = R =

? $12,000 $12,000 $12,000

Formulas:

PV – OA = R (PVF – OAn,i) PV – OA = R (PVF – OAn,i)

The present value of option (d) is $108,622 + $24,537, or

$187,470.

Present values:

(a) $200,000.

Time diagram:

i = 10%

PV – OA = ? R =

($71,000) ($71,000) $61,000 $61,000 $167,000 $167,000 $73,000 $73,000

Formulas:

PV – OA = R (PVF – OAn, i)

PV – OA =R (PVF – OAn, i)

PV – OA = ($71,000)(PVF – OA4, 10%)

PV – OA = $61,000 (PVF – OA10-4, 10%)

PV – OA = $167,000 (PVF – OA25–10, 10%)

PV – OA = $73,000 (PVF – OA40–25, 10%)

PV – OA = ($71,000)(3.16987)

PV – OA = $61,000 (6.14457 – 3.16987)

PV – OA = $167,000 (9.07704–6.14457)

PV – OA = $73,000 (9.77905 – 9.07704)

PV – OA = ($225,061)

PV – OA = $61,000 (2.97470)

PV – OA = $167,000 (2.93247)

PV – OA = $73,000 (0.70201)

PV – OA = $181,457

PV – OA = $489,722

PV – OA = $51,247

Present value of future net cash inflows:

Stacy Clark should accept no less than $497,365 for her vineyard business.

PROBLEM 6-7B

(a) Time diagram (alternative one):

i = ?

PV – OA =

$500,000 R =

$65,000 $65,000 $65,000 $65,000 $65,000

Formulas: PV – OA = R (PVF – OAn, i)

7.69 is present value of an annuity of $1 for 10 years discounted at

approximately 5%.

Time diagram (alternative two):

PROBLEM 6-7B (Continued)

Future value approach

Present value approach

FV = PV (FVFn, i)

PV = FV (PVFn, i)

Purple Cloud should choose alternative two since it provides a

higher rate of return.

(b) Time diagram:

i = ?

($1,450,000 – $290,000)

PV – OA = R =

PROBLEM 6-7B (Continued)

Formulas: PV – OA = R (PVF – OAn, i)

(c) Time diagram:

i = 6% per six months

PV = ?

PV – OA = R =

? $30,000 $30,000 $30,000 $30,000 $30,000 ($600,000 X 10% X 6/12)

Formulas:

Combined present value (amount received on sale of note):

$186,294 + $376,446 = $562,740

PROBLEM 6-7B (Continued)

(d) Time diagram (future value of $100,000 deposit)

i = 2% per quarter

PV =

$100,000 FV = ?

Amount to which quarterly deposits must grow:

$1,800,000 – $220,804 = $1,579,196.

Time diagram (future value of quarterly deposits)

PROBLEM 6-7B (Continued)

Formulas: FV – OA = R (FVF – OAn, i)