Question 2.S2.9: If ABC company expects cash inflows from its investment prop......
If ABC company expects cash inflows from its investment proposal it has undertaken in time period zero, Rs 2,00,000 and Rs 1,50,000 for the first two years respectively and then expects annuity payment of Rs 1,00,000 for the next eight years, what would be the present value of cash inflows, assuming a 10 per cent rate of interest?
We can solve the problem by applying the long method of finding the present values for each year’s amount by consulting Table A-3. But we would like to apply the short-cut procedure as most of the payments are part of an annuity. Table 2.9 presents the relevant calculations:
It may be noted that the present values (PV) of Rs 2,00,000 and Rs 1,50,000 (uneven cash flows) received at the end of the first and second years respectively are to be determined with reference to Table A-3. The present value of subsequent cash inflows of Rs 1,00,000 each for 8 years is found in Table A-4. The value of an annuity of Rs 1,00,000 for 8 years is found to be Rs 5,33,500. The most important point to note here is that Rs 5,33,500 is the present value at the beginning of the third year (end of year 2 ). Therefore, its present worth in time period zero would obviously be less than Rs 5,33,500. This amount would have to be discounted back for two years at 10 percent. The present value factor for 2 years at 10 per cent discount is 0.826. Multiplying this sum by Rs 5,33,500 we get Rs 4,40,671. When the present values of the first two payments are added to the present value of the annuity component, we obtain the sum of the present value of the entire investment. For a better understanding of the problem, a graphic representation of the procedure of calculating the present value (PV) of such a problem has been given in Fig. 2.3.
Table 2.9 Present Value of Uneven Cash Inflows Having Annuity
1. Present value of R s 2,00,000 due in year 1=(R s 2,00,000 \times 0.909)^{a}=R s \quad 1,81,800
Present value of Rs 1,50,000 due in year 2=(\text { Rs } 1,50,000 \times 0.826)^{a}= Rs 1,23,900
2. Present value of eight year annuity with \mathrm{Rs} 1,00,000 receipts:
(A) Present value at the beginning of year 3= Rs 1,00,000(5.335)^{b}= Rs 5,33,500
(B) Present value at the beginning of year 1=\operatorname{Rs} 5,33,500(0.826)=\operatorname{Rs} 4,40,671^{c}
3. Present value of total series =\mathrm{Rs} 7,46,371
{ }^{a} Present value factor at 10 per cent from Table A-3.
{ }^{b} Present value factor at 10 per cent from Table A-4.
{ }^{c}(6.145-1.736) \times \operatorname{Rs} 1,00,000