Where a busiess has two competig ivestmet opportuities the oe with the higher should be selected. Logically the value of a busiess should be the sum of all of the projects which it has i operatio at the particular time. ACTIVITY 3: QUESTION What is the of a ivestmet opportuity which ivolves a immediate outflow of 260,000, which will give rise to a iflow of 300,000 after oe year, assumig a iterest rate of 8%? ACTIVITY 3: ANSWER 300,000 = 260,000 + 8 1 + 100 = 260,000 + = 17,778 277,778 All other thigs beig equal, the ivestmet should be udertake. ACTIVITY 4: QUESTION What is the of a opportuity which ivolves receivig 10m immediately ad payig 12m after oe year assumig a 12% p.a. iterest rate? ACTIVITY 4: ANSWER 12m = 10m + 12 1 + 100 = 10m - 10.7 = - 0.7m The ivestmet should ot be udertake. Note that this discoutig approach is just as valid irrespective of whether the future cash flow is a positive or a egative oe. Maagemet Accoutig Diploma Course Sample Pages Page 1
Ivestmet Opportuities Lastig for More tha Oe Year I reality, few ivestmet opportuities last for oly oe year. Suppose that a ivestmet opportuity ivolves a immediate cash outflow C 0 which will give rise to iflows C 1 ad C 2 after oe ad two years respectively. We already kow that the preset value of C 1 (effect o the value of the busiess), is C 1 /(1 + i). By the same logic as we derived this, a amout, say Y, which would grow with iterest compouded aually to C 2. Y ivested ow will grow to Y + Yi or Y(1 + i) after oe year. Durig the secod year this amout Y 1 + i + Y 1 + i i. This equals will be re-ivested ad it will the grow to ( ) ( ( ) ) C 2 = Y + Yi + (Y + Yi)i (i.e. the origial borrowig plus iterest o that amout for the first year plus iterest o these two durig the secod year). This expressio expads to: C 2 = Y + Yi + Yi + Yi 2 takig Y outside brackets: C 2 = Y(1 + 2i + i 2 ) C 2 = Y(1 + i) 2 ad Y = C2/(1 + i) 2 Followig this logic, it ca be show that the preset value of ay amout of cash receivable after years (C ) would be C /(1 + i). If we wish to defie i a formal, mathematical way, we ca say that the of ay ivestmet opportuity is give by: = = t C t= + ( i) 0 1 (where t is the life of the opportuity i years) If we wish to put it i plai Eglish, we ca say that the of a opportuity is the sum of all of the cash flows associated with it, each oe discouted accordig to how far ito the future it oe will occur. Maagemet Accoutig Diploma Course Sample Pages Page 2
Example 2 Atoio plc has estimated that it could achieve cost savigs by ivestig i either of two automatic machies. The accoutat s estimate of the actual savigs ad of the cost of the machies is as follows: Type Alpha Type Beta Cost of the machie (payable ow) 50,000 60,000 Estimated aual savigs: Year 1 2 12,000 3 12,000 4 14,000 5 Which, if either, of these two machies should be bought if the relevat iterest rate is 10% per aum throughout? Note that the savigs listed above are ot actual iflows (receipts) of cash. They are however opportuity cash iflows. As such, we should recall from Uit 2, they are highly relevat to the preset decisio. Maagemet Accoutig Diploma Course Sample Pages Page 3
The of each machie is as follows: Type Alpha Type Beta Preset value of cash flows: Now (Year 0) (50,000) (60,000) 1 2 3 4 5 1 = 14,545 ( + 0.10) 12,000 9,917 12,000 2 = 9,016 3 = 6,830 4 = 14,000 5 = 6,209 = 14,545 2 = 3 = 4 = 5 = 13,223 12,021 9,562 6,209 (3,484) (4,440) This process of covertig future cash flows to their preset value is kow as discoutig. Tables are readily available which give the factor 1/(1 + i) for a rage of values of i ad. Such a table appears o the very last page of this uit. However, it is ot really worth botherig to use a table whe it is just as easy to use a calculator to discout from first priciples. It ca be see that both machies have a egative. To purchase either machie would reduce the value of the busiess. Neither of these two machies should, therefore, be bought o the basis of these estimates of costs (icludig the relevat iterest rate) ad of the beefits. ACTIVITY 5: QUESTION The supplier of the Alpha type machie has told Atoio plc that it might be prepared to reduce the price of the machie. O the basis of the above calculatios, what is the maximum price that Atoio plc should logically be prepared to pay for a machie? Maagemet Accoutig Diploma Course Sample Pages Page 4
ACTIVITY 5: ANSWER The maximum price which the busiess should be prepared to pay is the value of the savigs which would be expected to result from buyig the machie; it would be illogical to pay more for a ecoomic asset tha it is worth. To do so would reduce the value of the busiess, which is precisely the opposite of what busiesses seek to do. O the basis of the above calculatios, a Alpha type machie is worth 46,517 (i.e. the sum of the preset values of the savigs). It may be to aother busiess, or eve to Atoio plc uder other circumstaces, the machie may be worth more or less tha this. You should ote that the value of ay ecoomic asset should logically be deduced i this way. Advatages of Usig the Approach We ca coclude that is a valuable meas of assessig ivestmet opportuities because: It is directly derived from, what appears to be the mai fiacial objective of private sector orgaisatios It seems to take accout of all the relevat, measurable iformatio about a ivestmet opportuity. This icludes the timig of the estimated cash flows ad the cost of fiacig the ivestmet It gives clear uambiguous results, which are simple ad logical to iterpret. Discoutig ad Impoudig We have see that the major objective of discoutig future cash flows is to express all cash flows, irrespective of whe i the future they are estimated to occur, i the same terms so that a compariso ca be made. (Remember our origial problem i Example 1 was tryig to compare 1,000 to be spet immediately with 1,500 to be received a year later). A alterative to discoutig, i.e. expressig all cash flows i preset value terms, is to compoud, ie to express all cash flows i terms of their value at some specific date i the future. If, as we previously did i respect of Example 1, we assume a iterest rate of 10%, we should compoud the preset cash flow by addig 10% iterest to it ad the compare it with the uadjusted future cash flow. Maagemet Accoutig Diploma Course Sample Pages Page 5