Question

Desh Fashion is a Bangladeshi garment factory producing clothes for men, women, and children for European and American retailers. Over the last few years, it has made a substantial amount of profit as the demand for fast fashion has been significantly increasing among young people, in particular. However, recently the company is facing some uncertainties because of the trade war between China and America in addition to Brexit related tensions. Desh Fashion is losing its profitability since the beginning of 2018. To minimise the uncertainties it is facing and secure profit, Desh Fashion has decided to introduce its product to the Asian market, mainly in China.

To pursue the company’s dream, the Managing Director (MD) is considering acquiring a few local factories that produce fast fashion for the local market. The top-management approves the decision and prepares a proforma financial statement for the next five years. In the following table, the first three years expected revenues and their probabilities are presented.

Year	Revenue (£, 000)	Probability
2021	520	40%
	550	30%
	600	20%
	610	10%
2022	740	40%
	780	25%
	800	20%
	820	15%
2023	900	25%
	940	35%
	970	18%
	1,000	22%

[CONTINUED]

The respective costs for 2021 are provided below:

Description	Amount (£, 000)
Direct materials cost	125
Direct labour cost	80
Variable manufacturing overhead expense	30
Variable selling and administrative expense	20
Fixed overhead cost	200
Fixed selling and administrative expense	50

The MD is also expecting the following changes to costs in the coming years:

• The cost of direct materials will increase by 10% (compounding) per year.   
• The cost of labour will increase by 7.5% (compounding) per year.
• The variable manufacturing cost will keep increasing at the compounding rate of 8% per year.
• The variable selling and administrative expense will increase by 5% (compounding) per year.
• The company is expecting to have to buy new machineries which will cost £100,000 in 2022 and £150,000 in 2023.
• The fixed selling and administrative expenses are expected to increase at the compounding rate of 10% per year.
• The company is expected to pay 15% tax on net profit in 2021. This will increase to 25% from 2022 to onwards.

    

Required:

1. Calculate the expected value of sales and the standard deviation for 2021, 2022 and 2023.

Answer 1

Expected Value of Sales or Expected Return

Expected value of Sale is the weighted average of sales where weight represent probabilty

Expected Return of Sales  =( R1*P1)+(R2*P2)+( R3*P3)+............+( Rn*Pn)

Where

R = sales expectation

P= probability of that expectation

Standard Deviation

It is a Variation or dispersion around the most likely Expected Return of Sales (in this case)

Formula is Square root of Variance

Variance is the weighted average of squared differences from mean or expected return

Expected Value of sales for 2021

Revenue (R)	Probability (P)	R*P
520000	40%	208000 (520000*40%)
550000	30%	165000
600000	20%	120000
610000	10%	61000
	Total	554000

Expected value of sales 2021 is $554000

Standard Deviation of 2021

Revenue (R)	Probability (P)	Expected value or return (already calculated) (R!)	(R-R!)^2 * P
520000	40%	554000	462400000 (520000-554000)^2 * 40%
550000	30%	554000	4800000
600000	20%	554000	423200000
610000	10%	554000	313600000
		Total	1204000000

Standerd Deviation = Square root of 1204000000 =34698.703

Expected Value of sales for 2022

Revenue (R)	Probability (P)	R*P
740000	40%	296000
780000	25%	195000
800000	20%	160000
820000	15%	123000
	Total	774000

Expected value of sales 2022 is $774000

Standard Deviation of 2022

Revenue (R)	Probability (P)	Expected value or return (already calculated) (R!)	(R-R!)^2 * P
740000	40%	774000	462400000
780000	25%	774000	9000000
800000	20%	774000	135200000
820000	15%	774000	317400000
		Total	924000000

Standerd Deviation = Square root of 924000000 =30397.37

Expected Value of sales for 2023

Revenue (R)	Probability (P)	R*P
900000	25%	225000
940000	35%	329000
970000	18%	174600
1000000	22%	220000
	Total	9486000

Expected value of sales 2023 is $948600

Standard Deviation of 2023

Revenue (R)	Probability (P)	Expected value or return (already calculated) (R!)	(R-R!)^2 * P
900000	25%	948600	590490000
940000	35%	948600	25886000
970000	18%	948600	82432800
1000000	22%	948600	581231200
		Total	1280040000

Standerd Deviation = Square root of 1280040000 = 35777.65