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Solutions Manual

CHAPTER 21-FINANCIAL RISK MANAGEMENT II. Multiple Choice Questions 1.

D

2.

D

3.

B

Problem 3 Probability 0.10 0.30 0.30 0.20 0.10 1.00

Sales Volume (units)

Expected Sales Volume (units)

2,000 6,000 8,000 10,000 14,000

200 1,800 2,400 2,000 1,400 7,800

EV of contribution Less: Additional fixed overhead EV of additional cash profit per annum

[7,800 x (12 – 8)]

P31,200 20,000 P11,200

(a) Calculation of expected value of NPV of project Year 0 1–6 6 Expected NPV

Cash Flow P (40,000) 11,200 3,000

DCF @ 10%

PV of Cash Flow

1.0000 4.3550 0.5645

P (40,000) 48,776 1,694 P 10,470

(b) Calculation of minimum volume of sales per annum required to justify the project At break-even, the NPV would be zero. Taking the cost of the equipment and its residual value, the minimum required PV of annual cash profit would be as under: PV of capital outlay PV of residual value PV of actual cash profit required for NPV of 0

P40,000 1,694 P38,306

Discount factor of 1 per annum 6 years @ 10% is 4.355 Annual cash profit required Annual (cash) fixed costs

(P38,306/4.355)

P 8,796 20,000 P28,796 21-1

Chapter 21

Financial Risk Management

Annual contribution required for NPV = 0 Contribution per unit

= P4

Sales required to break-even: P28,796 P4

=

7,199 units

Problem 4 Annual cash inflow Less: Project cost Net present value

(P4,500 x 2.9137)

P13,112 12,000 P 1,112

(a) Sensitivity for Project Cost If the project cost is increased by P1,112, the NPV of the project will become zero. Therefore, the sensitivity for project cost is: P1,112 P12,000

x

100

=

9.27%

(b) Sensitivity for Annual Cash Inflow If the present value of annual cash inflow is lower by P1,112, the NPV of the project will become zero. Therefore, the sensitivity for annual cash flow is: P1,112 P13,112

x

100

=

8.48%

(c) Sensitivity for Cost of Capital Let “x” be the annuity factor which gives a zero NPV (i.e., “x” is the IRR) - P12,000 + P4,500 x P4,500 x x x

= = = =

0 P12,000 P12,000/P4,500 2.6667

Hence, x = 2.6667 and at 18% for 4 years, the annuity factor is 2.6667. Sensitivity %

=

18% − 14% 14%

=

29% 21-2

Financial Risk Management

Chapter 21

Analysis: The cash inflow is more sensitive, since only 8.5% change in cash inflow will make the NPV of the project zero. Problem 5 PV of Savings Year 1 (P60,000 x 0.9259) Year 2 (P70,000 x 0.8573)

P 55,554 60,011 P115,565

Less: PV of Running Cost Year 1 (P20,000 x 0.9259) Year 2 (P25,000 x 0.8573) Net savings Less: Purchase cost of plant Net present value

P18,518 21,432

39950 75,615 70,000 P 5,615

(a) Sensitivity for Plant Cost If the purchase cost of plant increases by P5,615, the NPV of the project will become zero. Therefore, the sensitivity for plant cost is: P5,615 P70,000

x

100

=

8.02%

(b) Sensitivity for Running Cost If the present value of running cost increases by P5,615, the NPV of the project will become zero. Therefore, the sensitivity for running cost is: P5,615 P39,950

x

100

=

14.06%

(c) Sensitivity for Savings If the savings decrease by P5,615, the NPV becomes zero. Therefore, the sensitivity for savings is: P5,615 P115,565

x

100

=

4.86%

Analysis: Savings is the most sensitive.

21-3

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CHAPTER 21-FINANCIAL RISK MANAGEMENT II. Multiple Choice Questions 1.

D

2.

D

3.

B

Problem 3 Probability 0.10 0.30 0.30 0.20 0.10 1.00

Sales Volume (units)

Expected Sales Volume (units)

2,000 6,000 8,000 10,000 14,000

200 1,800 2,400 2,000 1,400 7,800

EV of contribution Less: Additional fixed overhead EV of additional cash profit per annum

[7,800 x (12 – 8)]

P31,200 20,000 P11,200

(a) Calculation of expected value of NPV of project Year 0 1–6 6 Expected NPV

Cash Flow P (40,000) 11,200 3,000

DCF @ 10%

PV of Cash Flow

1.0000 4.3550 0.5645

P (40,000) 48,776 1,694 P 10,470

(b) Calculation of minimum volume of sales per annum required to justify the project At break-even, the NPV would be zero. Taking the cost of the equipment and its residual value, the minimum required PV of annual cash profit would be as under: PV of capital outlay PV of residual value PV of actual cash profit required for NPV of 0

P40,000 1,694 P38,306

Discount factor of 1 per annum 6 years @ 10% is 4.355 Annual cash profit required Annual (cash) fixed costs

(P38,306/4.355)

P 8,796 20,000 P28,796 21-1

Chapter 21

Financial Risk Management

Annual contribution required for NPV = 0 Contribution per unit

= P4

Sales required to break-even: P28,796 P4

=

7,199 units

Problem 4 Annual cash inflow Less: Project cost Net present value

(P4,500 x 2.9137)

P13,112 12,000 P 1,112

(a) Sensitivity for Project Cost If the project cost is increased by P1,112, the NPV of the project will become zero. Therefore, the sensitivity for project cost is: P1,112 P12,000

x

100

=

9.27%

(b) Sensitivity for Annual Cash Inflow If the present value of annual cash inflow is lower by P1,112, the NPV of the project will become zero. Therefore, the sensitivity for annual cash flow is: P1,112 P13,112

x

100

=

8.48%

(c) Sensitivity for Cost of Capital Let “x” be the annuity factor which gives a zero NPV (i.e., “x” is the IRR) - P12,000 + P4,500 x P4,500 x x x

= = = =

0 P12,000 P12,000/P4,500 2.6667

Hence, x = 2.6667 and at 18% for 4 years, the annuity factor is 2.6667. Sensitivity %

=

18% − 14% 14%

=

29% 21-2

Financial Risk Management

Chapter 21

Analysis: The cash inflow is more sensitive, since only 8.5% change in cash inflow will make the NPV of the project zero. Problem 5 PV of Savings Year 1 (P60,000 x 0.9259) Year 2 (P70,000 x 0.8573)

P 55,554 60,011 P115,565

Less: PV of Running Cost Year 1 (P20,000 x 0.9259) Year 2 (P25,000 x 0.8573) Net savings Less: Purchase cost of plant Net present value

P18,518 21,432

39950 75,615 70,000 P 5,615

(a) Sensitivity for Plant Cost If the purchase cost of plant increases by P5,615, the NPV of the project will become zero. Therefore, the sensitivity for plant cost is: P5,615 P70,000

x

100

=

8.02%

(b) Sensitivity for Running Cost If the present value of running cost increases by P5,615, the NPV of the project will become zero. Therefore, the sensitivity for running cost is: P5,615 P39,950

x

100

=

14.06%

(c) Sensitivity for Savings If the savings decrease by P5,615, the NPV becomes zero. Therefore, the sensitivity for savings is: P5,615 P115,565

x

100

=

4.86%

Analysis: Savings is the most sensitive.

21-3

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