Financial arithmetic for CF/IMCM

Question 1
If the rate of interest is 10%pa, and you have $1000 to invest:
(a) what will be its value after 10years on the basis of simple interest?
(b) as at (a) but interest is compounded once a year.
(c) after how long will the initial investment have doubled, on the basis of  (i) simple interest 
(ii) compound interest.  

Question 2
An investment of $1,000 now has the following cash flows. If the discount rate is (i) 12% (ii) 15%, what is the present value of these flows?
Year			Cash Flow
1			$ 200
2			   450
3			   600
4			   100
(a) Should the investment be undertaken in either of the above cases? 
(b) What is the cutoff discount rate for the investment? 

Question 3
Radlet  Enterprises has to make a decision between the following three investments:
(All figures in $’000 )
Year	Project A	Project B	Project C
0	-$ 100		-$100		-$100
1	+ $32		+$115		+166
2	+ $123		+$21		 -42
IRR        28%	             31%		35%
The Managing Director of the company prefers Project C. Which project would  you recommend to him if the cost of capital is 10%? 

Question 4
A firm is considering investment in Project A or Project B.  The project outlay and net cash inflows over the lives of the projects are estimated as below:
Project	A	B	
Year 0	-£100,000	-£100,000	
Year 1	£90,000	£30,000	
Year 2	£36,000	£104,000	

Required:
(i) Find the  NPV of  both projects at 10% and 20%
(ii) Use these figures to estimate the IRR.
(iii) Which project should the firm go ahead with if its cost of capital is 9%? Why?

Question 5
You have the following two offers from banks which are prepared to lend you
£10,000 now to be repaid in four equal payments at the end of  the first, second,
third and fourth years. 
Bank  P requires you to pay  £ 2,750 at  the end  of  each year . 
Bank  Q will calculate interest at 5% pa. 
Advise which of the above offers you will accept.

Question 6
Piccadilly Autos offers credit on a car which costs £10,000. A customer is required to pay £3,000 as down payment and the remainder at the rate of £2,000 a year, at the end of the year for the next four years.  General Auto next door does not offer credit on the same model but gives you a flat discount of £1,000. If the opportunity cost of finance is 10% which is the better deal? 

Question 7
You have leased a building for four years with a down payment of £20,000. You wish to rent this building over the same period. You have the following offers from two prospective clients:
- A will pay four equal payments of £6,000 at the end  of   each year for four years.
- B will pay in four equal instalments at the end of each year at 10% pa.
(i) Which offer gives you a higher return?
(ii) What is the rate of interest implied in A’s offer?

Question 8
A footballer has the following offers from two clubs: Club A will pay $3 million a year for the next 5 years; the first payment will be made at the end of the first year; Club B will pay $4 million now and then $2.2 million a year at the end of each year for the next 5 years. If  the rate of interest is 10%pa, which is the better offer?
 
Question 9
A financier is considering whether he should sponsor a rock concert project. This will involve an initial investment  of  £125,000 in preparation of  the site one year in advance of the event. Ticket revenues from the event are expected to be £200,000.  A cleanup and repair firm’s bills for repair and restoration of the site, post event are estimated at £50,000.  The cleanup firm will be paid one year after the event. Should the project be undertaken if the cost of capital is 10%?

Question 10
You are considering the purchase of a house. You expect to own the house for ten years at the end of which you will sell the house for $5 million. A finance company will lend you the sum to buy the house now but will require equal annual amounts every year to be paid from the end of the first year to the tenth year to include interest and capital repayment. What is the maximum price you can pay for the house now if the cost of finance is 12%?

Question 11
A finance company makes you the following offer: if you pay $100 a year, for the next ten years, from the beginning of next year, then they pay you $100 a year from the eleventh year forever. 
(a) Would you accept the proposal if the interest rate is (i) 9% (ii)  6% pa?
(b) What is the minimum interest rate that would make this proposal acceptable?

Question 12
(a) Calculate the future value of $100 received at the end of  every year for 10 years: the first payment to begin at the end of the first year, at the end of ten years.
(b) Rework question 10, on the basis of future value at the end of 10 years.
(c)  Rework question 11, on the basis of future value at the end of 10 years.

Question 13
You have $100 available for investment. You decide to invest some proportion in an asset R and some proportion in asset M. Asset R gives a return of 6%, and Asset M gives a return of 14%.  You risk preference level is satisfied at a return of 10%. Calculate the proportions you need to invest in asset R and asset M to obtain your desired return. 

Kvs/300908

Formulas

(1)  Net Present Value
	
	NPV  =         CFt	    
           (1 + k) t

(2)  Internal Rate of Return 

                          (R2-R1)  (NPV(R1))
IRR = R1 +    -------------------------------
			((NPV(R1)-NPV(R2)) 

(3) Future value:     FV  =  ((1+r) n  -1)/r

PRESENT VALUE TABLES								
											
Present value of 1$ received at the end of n years (=1/(1+r)^n)				
											
YEAR/r	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%	
1	0.990	0.980	0.971	0.962	0.952	0.943	0.935	0.926	0.917	0.909	
2	0.980	0.961	0.943	0.925	0.907	0.890	0.873	0.857	0.842	0.826	
3	0.971	0.942	0.915	0.889	0.864	0.840	0.816	0.794	0.772	0.751	
4	0.961	0.924	0.888	0.855	0.823	0.792	0.763	0.735	0.708	0.683	
5	0.951	0.906	0.863	0.822	0.784	0.747	0.713	0.681	0.650	0.621	
6	0.942	0.888	0.837	0.790	0.746	0.705	0.666	0.630	0.596	0.564	
7	0.933	0.871	0.813	0.760	0.711	0.665	0.623	0.583	0.547	0.513	
8	0.923	0.853	0.789	0.731	0.677	0.627	0.582	0.540	0.502	0.467	
9	0.914	0.837	0.766	0.703	0.645	0.592	0.544	0.500	0.460	0.424	
10	0.905	0.820	0.744	0.676	0.614	0.558	0.508	0.463	0.422	0.386	
11	0.896	0.804	0.722	0.650	0.585	0.527	0.475	0.429	0.388	0.350	
12	0.887	0.788	0.701	0.625	0.557	0.497	0.444	0.397	0.356	0.319	
13	0.879	0.773	0.681	0.601	0.530	0.469	0.415	0.368	0.326	0.290	
14	0.870	0.758	0.661	0.577	0.505	0.442	0.388	0.340	0.299	0.263	
15	0.861	0.743	0.642	0.555	0.481	0.417	0.362	0.315	0.275	0.239	
16	0.853	0.728	0.623	0.534	0.458	0.394	0.339	0.292	0.252	0.218	
17	0.844	0.714	0.605	0.513	0.436	0.371	0.317	0.270	0.231	0.198	
18	0.836	0.700	0.587	0.494	0.416	0.350	0.296	0.250	0.212	0.180	
19	0.828	0.686	0.570	0.475	0.396	0.331	0.277	0.232	0.194	0.164	
20	0.820	0.673	0.554	0.456	0.377	0.312	0.258	0.215	0.178	0.149	
											
YEAR/r	11%	12%	13%	14%	15%	16%	17%	18%	19%	20%	
1	0.901	0.893	0.885	0.877	0.870	0.862	0.855	0.847	0.840	0.833	
2	0.812	0.797	0.783	0.769	0.756	0.743	0.731	0.718	0.706	0.694	
3	0.731	0.712	0.693	0.675	0.658	0.641	0.624	0.609	0.593	0.579	
4	0.659	0.636	0.613	0.592	0.572	0.552	0.534	0.516	0.499	0.482	
5	0.593	0.567	0.543	0.519	0.497	0.476	0.456	0.437	0.419	0.402	
6	0.535	0.507	0.480	0.456	0.432	0.410	0.390	0.370	0.352	0.335	
7	0.482	0.452	0.425	0.400	0.376	0.354	0.333	0.314	0.296	0.279	
8	0.434	0.404	0.376	0.351	0.327	0.305	0.285	0.266	0.249	0.233	
9	0.391	0.361	0.333	0.308	0.284	0.263	0.243	0.225	0.209	0.194	
10	0.352	0.322	0.295	0.270	0.247	0.227	0.208	0.191	0.176	0.162	
11	0.317	0.287	0.261	0.237	0.215	0.195	0.178	0.162	0.148	0.135	
12	0.286	0.257	0.231	0.208	0.187	0.168	0.152	0.137	0.124	0.112	
13	0.258	0.229	0.204	0.182	0.163	0.145	0.130	0.116	0.104	0.093	
14	0.232	0.205	0.181	0.160	0.141	0.125	0.111	0.099	0.088	0.078	
15	0.209	0.183	0.160	0.140	0.123	0.108	0.095	0.084	0.074	0.065	
16	0.188	0.163	0.141	0.123	0.107	0.093	0.081	0.071	0.062	0.054	
17	0.170	0.146	0.125	0.108	0.093	0.080	0.069	0.060	0.052	0.045	
18	0.153	0.130	0.111	0.095	0.081	0.069	0.059	0.051	0.044	0.038	
19	0.138	0.116	0.098	0.083	0.070	0.060	0.051	0.043	0.037	0.031	
20	0.124	0.104	0.087	0.073	0.061	0.051	0.043	0.037	0.031	0.026	

											

ANNUITY TABLES									
											
Present value of 1$ received every year at the end of n years (=1/r(1- 1/(1+r)^n))	
											
YEAR/r	1%	2%	3%	4%	5%	6%	7%	8%	9%	10%	
1	0.990	0.980	0.971	0.962	0.952	0.943	0.935	0.926	0.917	0.909	
2	1.970	1.942	1.913	1.886	1.859	1.833	1.808	1.783	1.759	1.736	
3	2.941	2.884	2.829	2.775	2.723	2.673	2.624	2.577	2.531	2.487	
4	3.902	3.808	3.717	3.630	3.546	3.465	3.387	3.312	3.240	3.170	
5	4.853	4.713	4.580	4.452	4.329	4.212	4.100	3.993	3.890	3.791	
6	5.795	5.601	5.417	5.242	5.076	4.917	4.767	4.623	4.486	4.355	
7	6.728	6.472	6.230	6.002	5.786	5.582	5.389	5.206	5.033	4.868	
8	7.652	7.325	7.020	6.733	6.463	6.210	5.971	5.747	5.535	5.335	
9	8.566	8.162	7.786	7.435	7.108	6.802	6.515	6.247	5.995	5.759	
10	9.471	8.983	8.530	8.111	7.722	7.360	7.024	6.710	6.418	6.145	
11	10.368	9.787	9.253	8.760	8.306	7.887	7.499	7.139	6.805	6.495	
12	11.255	10.575	9.954	9.385	8.863	8.384	7.943	7.536	7.161	6.814	
13	12.134	11.348	10.635	9.986	9.394	8.853	8.358	7.904	7.487	7.103	
14	13.004	12.106	11.296	10.563	9.899	9.295	8.745	8.244	7.786	7.367	
15	13.865	12.849	11.938	11.118	10.380	9.712	9.108	8.559	8.061	7.606	
16	14.718	13.578	12.561	11.652	10.838	10.106	9.447	8.851	8.313	7.824	
17	15.562	14.292	13.166	12.166	11.274	10.477	9.763	9.122	8.544	8.022	
18	16.398	14.992	13.754	12.659	11.690	10.828	10.059	9.372	8.756	8.201	
19	17.226	15.678	14.324	13.134	12.085	11.158	10.336	9.604	8.950	8.365	
20	18.046	16.351	14.877	13.590	12.462	11.470	10.594	9.818	9.129	8.514	
											
YEAR/r	11%	12%	13%	14%	15%	16%	17%	18%	19%	20%	
1	0.901	0.893	0.885	0.877	0.870	0.862	0.855	0.847	0.840	0.833	
2	1.713	1.690	1.668	1.647	1.626	1.605	1.585	1.566	1.547	1.528	
3	2.444	2.402	2.361	2.322	2.283	2.246	2.210	2.174	2.140	2.106	
4	3.102	3.037	2.974	2.914	2.855	2.798	2.743	2.690	2.639	2.589	
5	3.696	3.605	3.517	3.433	3.352	3.274	3.199	3.127	3.058	2.991	
6	4.231	4.111	3.998	3.889	3.784	3.685	3.589	3.498	3.410	3.326	
7	4.712	4.564	4.423	4.288	4.160	4.039	3.922	3.812	3.706	3.605	
8	5.146	4.968	4.799	4.639	4.487	4.344	4.207	4.078	3.954	3.837	
9	5.537	5.328	5.132	4.946	4.772	4.607	4.451	4.303	4.163	4.031	
10	5.889	5.650	5.426	5.216	5.019	4.833	4.659	4.494	4.339	4.192	
11	6.207	5.938	5.687	5.453	5.234	5.029	4.836	4.656	4.486	4.327	
12	6.492	6.194	5.918	5.660	5.421	5.197	4.988	4.793	4.611	4.439	
13	6.750	6.424	6.122	5.842	5.583	5.342	5.118	4.910	4.715	4.533	
14	6.982	6.628	6.302	6.002	5.724	5.468	5.229	5.008	4.802	4.611	
15	7.191	6.811	6.462	6.142	5.847	5.575	5.324	5.092	4.876	4.675	
16	7.379	6.974	6.604	6.265	5.954	5.668	5.405	5.162	4.938	4.730	
17	7.549	7.120	6.729	6.373	6.047	5.749	5.475	5.222	4.990	4.775	
18	7.702	7.250	6.840	6.467	6.128	5.818	5.534	5.273	5.033	4.812	
19	7.839	7.366	6.938	6.550	6.198	5.877	5.584	5.316	5.070	4.843	
20	7.963	7.469	7.025	6.623	6.259	5.929	5.628	5.353	5.101	4.870