In: Finance
First Question | |||||||||||||
Deposit monthly | 500 | ||||||||||||
Rate of interest per year | 8% | ||||||||||||
Monthly compunded rate of return =(((1.08)^(1/12))-1))*100 | 0.643403 | ||||||||||||
Time period in months | 120 | ||||||||||||
Future value | 1079.462 | ||||||||||||
Second Question | |||||||||||||
Initial investment | 50000 | ||||||||||||
Terminal value | 45000 | ||||||||||||
Rate of return | 12% | ||||||||||||
Particulars | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8th year included (Cash flow and terminal value=8500+45000) | ||||
Cash flows | 6000 | 6500 | 7000 | 7500 | 7500 | 8500 | 8500 | 53500 | |||||
Discount factor | 1.12 | 1.2544 | 1.404928 | 1.573519 | 1.762342 | 1.973823 | 2.210681 | 2.475963176 | |||||
Present value | 5357.143 | 5181.76 | 4982.462 | 4766.386 | 4255.701 | 4306.365 | 3844.968 | 21607.7527 | |||||
Sum of present value | 54302.54 | ||||||||||||
NPV | 4302.537 | ||||||||||||
As NPV is positive it is a good investment | |||||||||||||
Part A if rate of return is 15% | 15% | ||||||||||||
Particulars | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8th year included (Cash flow and terminal value=8500+45000) | ||||
Cash flows | 6000 | 6500 | 7000 | 7500 | 7500 | 8500 | 8500 | 53500 | |||||
Discount factor (1+r)^n | 1.15 | 1.3225 | 1.520875 | 1.749006 | 2.011357 | 2.313061 | 2.66002 | 3.059022863 | |||||
Present value | 5217.391 | 4914.934 | 4602.614 | 4288.149 | 3728.826 | 3674.785 | 3195.465 | 17489.2449 | |||||
Sum of present Value | 47111.41 | ||||||||||||
NPV | -2888.59 | ||||||||||||
As NPV is negative it is a profitable business | |||||||||||||
Part B if rate of return is 8% | 8% | ||||||||||||
Particulars | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8th year included (Cash flow and terminal value=8500+45000) | ||||
Cash flows | 6000 | 6500 | 7000 | 7500 | 7500 | 8500 | 8500 | 53500 | |||||
Discount factor (1+r)^n | 1.08 | 1.1664 | 1.259712 | 1.360489 | 1.469328 | 1.586874 | 1.713824 | 1.85093021 | |||||
Present value | 5555.556 | 5572.702 | 5556.826 | 5512.724 | 5104.374 | 5356.442 | 4959.668 | 28904.38532 | |||||
Sum of present value | 66522.68 | ||||||||||||
NPV | 16522.68 | ||||||||||||
As NPV is positive it is a good investment | |||||||||||||
Third Question | |||||||||||||
Internal rate of return | 13.7215% | ||||||||||||
Particulars | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 8th year included (Cash flow and terminal value=8500+45000) | ||||
Cash flows | 6000 | 6500 | 7000 | 7500 | 7500 | 8500 | 8500 | 53500 | |||||
Discount factor (1+r)^n | 1.137215 | 1.293258 | 1.470712 | 1.672516 | 1.90201 | 2.162995 | 2.45979 | 2.797310243 | |||||
Present value | 5276.047 | 5026.066 | 4759.598 | 4484.262 | 3943.196 | 3929.737 | 3455.579 | 19125.51535 | |||||
Sum of present value | 50000 | ||||||||||||
IRR is that rate for which NPv is 0 | 13.7215% | ||||||||||||
Fourth Question | |||||||||||||
Annual payments | 50000 | ||||||||||||
Time period | 20 | ||||||||||||
Rate of return | 12% | ||||||||||||
Present value | |||||||||||||
Particulars | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
Payment | 50000 | 50000 | 50000 | 50000 | 50000 | 50000 | 50000 | 50000 | 50000 | 50000 | 50000 | 50000 | |
Discount factor (1+r)^n | 1.12 | 1.2544 | 1.404928 | 1.573519 | 1.762342 | 1.973823 | 2.210681 | 2.475963176 | 2.773079 | 3.105848 | 3.47855 | 3.895976 | |
Present value | 44642.86 | 39859.69 | 35589.01 | 31775.9 | 28371.34 | 25331.56 | 22617.46 | 20194.1614 | 18030.5 | 16098.66 | 14373.81 | 12833.75 | |
Sum of Present value | 309718.7 | ||||||||||||
As the present value which is 309718.7 is less than 400000 I should take the lump sum payment right away as there 400000 invested now at 12% will yield higher than the lottery prize money | |||||||||||||
Fifth question | |||||||||||||
Present value | 10000 | ||||||||||||
Final value | 18000 | ||||||||||||
rate of return in months | r | ||||||||||||
time period in months | 60 | ||||||||||||
So 18000=10000(1+r)^60 | |||||||||||||
(1+r)^60 | 1.8 | ||||||||||||
1+r | 1.009845 | ||||||||||||
r= | 0.009845 | ||||||||||||
r (in %) | 0.984459 | ||||||||||||
Sixth question | |||||||||||||
Part A | |||||||||||||
Payment deposited annually C | 2000 | ||||||||||||
Rate of interest | 10% | ||||||||||||
Final value | 100000 | 20000 | 100000 | 5 | 6 | ||||||||
Future value of annuity is given by ((C/r)*(((1+r)^n)-1))=100000 | 1.791759469 | 0.09531 | |||||||||||
18.7992455 | |||||||||||||
So n | 18.8 | ||||||||||||
It will take 18 years and 8 months to accumulate 100000 | |||||||||||||
Part B | |||||||||||||
C | ? | ||||||||||||
r | 10% | ||||||||||||
n | 5 | ||||||||||||
Final value | 100000 | ||||||||||||
Applying the same concept of annuity and formula as shown above | 1.61051 | 0.61051 | 6.1051 | 16379.75 | |||||||||
(1+r)^n | 1.61051 | ||||||||||||
X=((1+r)^n)-1 | 0.61051 | ||||||||||||
X/r | 6.1051 | ||||||||||||
C | 16379.75 |