Chapter 21 - Answer

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CH

CHAPAPTER TER 2121

FI

FINANNANCICIAL AL RIRISK SK MMANAGANAGEMEMENTENT

S

SUGGESTEDUGGESTED A ANSWERSNSWERS TOTO THETHE R R EVIEWEVIEW Q QUESTIONSUESTIONS ANDAND P PROBLEMSROBLEMS I.

I. QuestionsQuestions 1.

1. ReRefefer tr to o papage ge 52520.0. 2.

2. RefRefer er to to pagpages es 520 520 thrthrougough 5h 52121.. 3.

7. RefRefer er to to pagpages es 527 527 thothough ugh 528528.. 8.

9. RefRefer ter to po pageages 5s 538 t38 throhrough ugh 539539.. 1

100.. AA decision treedecision tree is an analytical tool used in a prole! in "hich a series is an analytical tool used in a prole! in "hich a series of decision has to e !ade at #arious ti!e inter#als$ "ith each decision of decision has to e !ade at #arious ti!e inter#als$ "ith each decision influenced y the infor!ation that is a#ailale at the ti!e

influenced y the infor!ation that is a#ailale at the ti!e it is !ade.it is !ade. %he decision ranches "ill e dra"n as ro&en lines e!erging fro! %he decision ranches "ill e dra"n as ro&en lines e!erging fro! s'uare nodes and the outco!es of a trail as solid lines e!erging fro! s'uare nodes and the outco!es of a trail as solid lines e!erging fro! round nodes. %he s'uare nodes$ fro! "hich the decision ranches are round nodes. %he s'uare nodes$ fro! "hich the decision ranches are dra"n$ represent the points at "hich decision !a&er selects his decision. dra"n$ represent the points at "hich decision !a&er selects his decision. %he round node

%he round nodes s reprepresresent the ent the poipointnts s at at "hi"hich ch the outcthe outco!o!e e of of thethe decision arises. %he decision !a&er has no control o#er the outco!e and decision arises. %he decision !a&er has no control o#er the outco!e and can

can onlonly y estesti!i!ate ate the the proproaailiility ty of of the the #ar#ariouious s ououtcotco!es !es actactuauallylly occurring. (hen all of the decisions and

occurring. (hen all of the decisions and outco!es ha#e een representedoutco!es ha#e een represented on the tree$ each of the possile routes through tree is considered and the on the tree$ each of the possile routes through tree is considered and the !onetary payoff is sho"n at the end of

!onetary payoff is sho"n at the end of each route. Any costs incurred yeach route. Any costs incurred y the decisions are indicated along

the decisions are indicated along the appropriate ranches.the appropriate ranches. II.

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III. Problems P"o%l!& $ Expected Profit: +roduct , - 0.20 / +8$000  0.10 / +5$000  0.30 +11$000  0.20 +14$000  0.20 +17$000 - +7$400 +roduct  - 0.15 / +12$000  0.15 / +10$000  0.40 +14$000  0.20 +16$000  0.10 +18$000 - +7$300 Analysis:

*ased on the ao#e data$ the choice "ill e !ade for +roduct ,. P"o%l!& #

a %o rea&/e#en$ the co!pany !ust earn enough total contriution to co#er its fied costs. %he contriution to fied costs and profits is +2.50 per unit +6  3.5 per unit.

%o rea&/e#en$ sales !ust e as follo"s

%he proaility that sales "ill e'ual or eceed 13$600 units is the proaility that sales "ill e 14$000$ 16$000 or 18$000 units$ "hich is

0.25  0.30  0.20 - 0.75 or 75.

 %o earn profit of +10$000$ the co!pany !ust earn enough contriution to co#er its fied costs +34$000 and then !a&e the profit$ so total contriution !ust e +44$000. %o earn this contriution$ sales !ust e as follo"s

%he proaility that sales "ill e'ual or eceed 17$600 units is the proaility of sales eing 18$000 units$ "hich is 0.20 or 20.

ontriution re'uired ontriution per unit

+34$000 +2.50

- - 13$600 units

+44$000

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P"o%l!& ' Probability Sales Volume (units) Expecte Sales Volume (units) 0.10 2$000 200 0.30 6$000 1$800 0.30 8$000 2$400 0.20 10$000 2$000 0.10 14$000 1$400 1.00 7$800  of contriution :7$800  12  8; +31$200

<ess Additional fied o#erhead 20$000

 of additional cash profit per annu! +11$200

(a) Calculation of expected value of NPV of project

!ear Cash Flo" #CF $ %&' PV o Cash Flo"

0 + 40$000 1.0000 + 40$000

1  6 11$200 4.3550 48$776

6 3$000 0.5645 1$694

pected=+ + 10$470

(b) Calculation of minimum volume of sales per annum required to justify te project

At rea&/e#en$ the =+ "ould e >ero. %a&ing the cost of the e'uip!ent and its residual #alue$ the !ini!u! re'uired + of annual cash profit "ould e as under

+ of capital outlay +40$000

+ of residual #alue 1$694

+ of actual cash profit re'uired for =+ of 0 +38$306

)iscount factor of 1 per annu! 6 years ? 10 is 4.355

Annual cash profit re'uired [email protected] + 8$796

Annual cash fied costs 20$000

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Annual contriution re'uired for =+ - 0 ontriution per unit - +4 ales re'uired to rea&/e#en

P"o%l!& (

Annual cash inflo" +4$500  2.9137 +13$112

<ess +roBect cost 12$000

=et present #alue + 1$112

(a) !ensitivity for Project Cost

Cf the proBect cost is increased y +1$112$ the =+ of the proBect "ill eco!e >ero. %herefore$ the sensiti#ity for proBect cost is

(b) !ensitivity for Annual Cas "nflo#

Cf the present #alue of annual cash inflo" is lo"er y +1$112$ the =+ of the proBect "ill eco!e >ero. %herefore$ the sensiti#ity for annual cash flo" is

(c) !ensitivity for Cost of Capital

<et $x% e the annuity factor "hich gi#es a >ero =+ i.e.$ $x% is the CRR

/ +12$000  +4$500  - 0

+4$500  - +12$000

 - +12$000@+4$500  - 2.6667

Dence$ x - 2.6667 and at 18 for 4 years$ the annuity factor is 2.6667.

+28$796 +4 - 7$199 units +1$112 +12$000  100 - 9.27 +1$112 +13$112  100 - 8.48 29 18 E 14 14 - -ensiti#ity 

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Analysis:

%he cash inflo" is !ore sensiti#e$ since only 8.5 change in cash inflo" "ill !a&e the =+ of the proBect >ero.

P"o%l!& )

+ of a#ings

ear 1 +60$000  0.9259 + 55$554

ear 2 +70$000  0.8573 60$011

+115$565 <ess + of Running ost

ear 1 +20$000  0.9259 +18$518

ear 2 +25$000  0.8573 21$432 39950

=et sa#ings 75$615

<ess +urchase cost of plant 70$000

=et present #alue + 5$615

(a) !ensitivity for Plant Cost

Cf the purchase cost of plant increases y +5$615$ the =+ of the proBect "ill eco!e >ero. %herefore$ the sensiti#ity for plant cost is

(b) !ensitivity for &unnin' Cost

Cf the present #alue of running cost increases y +5$615$ the =+ of the proBect "ill eco!e >ero. %herefore$ the sensiti#ity for running cost is

(c) !ensitivity for !avin's

Cf the sa#ings decrease y +5$615$ the =+ eco!es >ero. %herefore$ the sensiti#ity for sa#ings is

Analysis: 8.02 +5$615 +70$000  100 -14.06 +5$615 +39$950  100 -4.86 +5$615 +115$565  100

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