深圳大学管理学院：《运筹学》课程教学资源（PPT课件讲稿）决策与对策（决策论）运筹学3类 CAPITAL INVESTMENT DECISIONS

CHAPTER12. CAPITAL INVESTMENT DECISIONS

CHAPTER12: CAPITAL INVESTMENT DECISIONS

INTRODUCTION a Linear programming models a company has finite production capacity(machinery resource constraints If the demand suddenly increase, the company would be unable to meet this extra demand without increasing the amount of machine time that is available for production One way of meeting the additional product demand is for the company to buy a piece of machinery with greater production capacity. a Buying new equipment involves decisions making over future planning time periods

INTRODUCTION ◼ Linear programming models ❑ company has finite production capacity (machinery resource constraints) ❑ If the demand suddenly increase, the company would be unable to meet this extra demand without increasing the amount of machine time that is available for production ❑ One way of meeting the additional product demand is for the company to buy a piece of machinery with greater production capacity. ❑ Buying new equipment involves decisions making over future planning time periods

Break-Even model a Production capacity of the company is limited(250 units of output per production time period) a If the demand for the company' s product is greater than 250 units, then the company would be faced with the dilemma of how to handle this excess demand For a short -term increased demand Introducing overtime working Raising the price of the product a For a long-term increased demand Expanding the existing production facilities Building a bigger scale production plant a Company is faced with a decision which involves the costs and benefits that will accrue to the company over some future time horizon

◼ Break-Even model ❑ Production capacity of the company is limited (250 units of output per production time period). ❑ If the demand for the company's product is greater than 250 units, then the company would be faced with the dilemma of how to handle this excess demand. ❑ For a short-term increased demand ◼ Introducing overtime working ◼ Raising the price of the product ❑ For a long-term increased demand ◼ Expanding the existing production facilities ◼ Building a bigger scale production plant. ❑ Company is faced with a decision which involves the costs and benefits that will accrue to the company over some future time horizon

COMPOUNDING Notation for different time periods (yearly basis) a to -to stands for time period zero and represents right now; a t1 ---to stands for time period one and represents 1 year into the future a t2---to stands for time period two and represents 2 years into the future a tn---to stands for time period n and represents n years into the future where n can take on any value from 0.1.2

COMPOUNDING ◼ Notation for different time periods (yearly basis) ❑ t0 --- to stands for time period zero and represents right now; ❑ t1 ---to stands for time period one and represents 1 year into the future; ❑ t2 ---to stands for time period two and represents 2 years into the future; ❑ tn ---to stands for time period n and represents n years into the future , where n can take on any value from 0,1,2

Initial capital or lump sum o a financial investor has a sum of money to invest in time period to, for example f100 a If the investor deposits his f100 in an interest bearing bank account, how much will he have after 1 year a Suppose: the going rate of interest is 10%

◼ Initial capital or lump sum ❑ A financial investor has a sum of money to invest in time period t0, for example £100 ❑ If the investor deposits his £100 in an interest bearing bank account, how much will he have after 1 year. ❑ Suppose: the going rate of interest is 10%

a For year 1, the value of the investment to the investor a(what he starts with)+( the interest on what he starts With ￡100+10%X100=￡100(1+10%)=￡110 o to--10%->t1 100->100+10%of100 =100(1+10%) =2110

◼ For year 1, the value of the investment to the investor: ❑ (what he starts with) + (the interest on what he starts with) ❑ £100 + 10%x£100 = £100(1+10%) = £110 ❑ t0—10%—>t1 100 —> 100+10% of 100 = 100(1+10%) =£110

For year 2, the value of the investment to the investor, a what he starts with at the beginning of year 2)+(the interest earned over year 2) ￡110+10%X110=￡110(1+10%)=￡121 10%—>t-10%—>t2 100→>100+10%X00 =100(1+10%) 110 >110+10%X|10 =1101+10%) =2121 a110(1+10%)=100(+109%)(+10%) =100(+10%)2 =￡121

◼ For year 2, the value of the investment to the investor: ❑ (what he starts with at the beginning of year 2) + (the interest earned over year 2) ❑ £110 +10%x£l 10 = £110(1+10%) = £121 t0 —10% —> t1 —10% —> t2 100 —> 100+10%xl00 =100(1+10%) =110 —> 110+10%x l10 = 110(1+10%) =£121 ❑ 110(1+10%) = 100(l+10%)(l+10%) = 100(l+10%)2 = £121

For year 3 the value of the investment to the investor ato-10%>t1-10%—>t2-10%>t 100 >100+10%X00 =1001+10%) =110->110+10%X0 =1101+10%) =100(1+10%)2 =121>121+10%X21 121(1+10%) =100(+10%)3 =2133.1

◼ For year 3, the value of the investment to the investor: ❑ t0 —10%—> t1 —10%—> t2 —10%—> t3 100 —> 100+10%xl00 =100(1+10%) = 110 —> 110+10%xll0 = 110(1+10%) =100(1+10%)2 =121 —> 121+10%xl21 =121(1+10%) =100(l+10%)3 =£133.1

a The value of the investment at different time periods can be summarised as follows >t -->t 100100+10%)1100(+10%)2100(+10%) For year n, General compounding idea as follows a For a given initial lump sum A a For a given term of investment n a For a given rate of interest 1% a Future value(Fv of the investment is given by a FV=A(+i%)n

◼ The value of the investment at different time periods can be summarised as follows: ❑ t0 ----------> t1 -------------> t2 -------------> t3 100 100(l+10%)1 100(l+10%)2 100(l+10%)3 ◼ For year n, General compounding idea as follows: ❑ For a given initial lump sum A ❑ For a given term of investment n ❑ For a given rate of interest i% ❑ Future value (FV) of the investment is given by: ❑ FV = A(l+i%)n

DISCOUNTING Discounting is the reverse side of the coin to compounding With discounting the time direction is reversed For the value of a sum of money in the future, we want to know what this future sum is worth to us right now Considering the position of a money lender, Aclient would like to borrow some money in order to finance some immediate expenditure however the client does have an asset that will be available, not to-day, but in 1 years time. At this time the asset will have a value of f100. thus the client has an asset -E100 available in one years time-but unfortunately for him he wants money NoW The client can thus pose the following question to the money lender

DISCOUNTING ◼ Discounting is the reverse side of the coin to compounding ◼ With discounting the time direction is reversed. ◼ For the value of a sum of money in the future, we want to know what this future sum is worth to us right now. ◼ Considering the position of a money lender, A client would like to borrow some money in order to finance some immediate expenditure, however the client does have an asset that will be available , not to-day, but in 1 years time. At this time the asset will have a value of £100. Thus the client has an asset - £100 available in one years time -but unfortunately for him he wants money NOW. The client can thus pose the following question to the money lender: