Response 1: Concept of cash flow
In corporate finance, the concept of cash flow denotes the money that moves in an out of a business or associated with an investment in a specified period of time like a month or a year. For instance, cash can either flow in or out of the business. Cash inflow entails the money that flows from your clients or customers from consuming the products of a business (Day, 2012). For investments, cash inflow may indicate the savings associated with the investment or the cash reaped during its operations. Contrary, cash outflows include the money that goes out of a business in form of meeting obligations such as expenses. Good examples of these expenses include monthly loan repayments Schroeder, Clark, & Cathey, 2001). Firms ensure that they always have balanced cash flow to avoid issues where they run out of cash to run their daily activities.
Response 2: Relationship of present value and future value
The present value indicates the worth of a particular sum of money or investment in contrast to some future value which it will have supposed it was invested at a compound interest. It gives the net worth of future streams of cash flows in as if it existed today (Day, 2012). Contrary, the future value indicates the present worth plus the interest that is earned from owning a particular sum of money or interest earning investment. The main relationship here is that both the PV and FV measure the worth change of money over a specified time (Shim, 2012). The FT is determined by multiplying the PV of a cash flow by the accumulation function.
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Response 3: Present value and interest rates
The present value is influenced by interest rates in that as the interest rates increase, the PV decreases. The interest rate is used to discount the future streams of cash flows to determine their present worth (Day, 2012). Ideally, the interest rate is used to compute the present value interest factor (PVIF) and forms the multiplier used to calculate the PV of cash flows. The PV and the interest rate have an inversely proportional relationship because the PVIF reduces with increasing interest rate (Helfert, 2003). Since the PVIF is multiplied with the future value of any cash flow to determine its present worth, reducing PVIF as a result of reducing interest rate, denotes a decreasing PV.
Problem Solutions
Solution 1 (Using Excel formula)
|
Three Scenarios |
|||
| Rate at 4% | Rate at 6% | Rate at 7% | |
| Present Value | $ 250 | $ 250 | $ 250 |
| Discounting rate |
4% |
6% |
7% |
| nper (time) |
9 |
9 |
9 |
| pmt |
0 |
0 |
0 |
| Future Value (Excel formula = FV(Rate,nper,pmt,-PV,0) |
$355.83 |
$422.37 |
$459.61 |
Based on the above analysis, it is clear that the future value of the $250 deposited in a savings account increase with an increase interest rate with time remaining constant. At 4% interest rate the FV is $355.83 which grows to $459.61 when the rate is adjusted to 7%.
Solution 2 (Using algebra approach)
Future value of $450 deposit earning different interest annually for three years
Present value = $450
Interest rate year 1 = 6%
Interest rate year 2 = 3%
Interest rate year 3 = 7%
Future value = Present Value * (1+r)^n ;
Where r = interest rate per period and n = number of periods
FV = 450 * (1+6%) * (1+3%) * (1+7%)
= $525.70
Solution 3: Rate of return using algebra approach
Scenario 1: 5 year’s growth
FV = PV * (1+r)n but PV is given as $8,000 and FV is given as $12,500
12,500 = 8,000 * (1 + r)5
1.5625 = (1 + r)5
1 + r = (1.5625)1/5
Solving for r;
Rate or r = 9.33%
Scenario 2: 6 year’ growth
FV = PV * (1+r)n
12,500 = 8,000 (1 + r)6
1.5625 = (1+r)6
1 + r = (1.5625)1/6
Solving for r = 7.69%
Scenario 3: 8 year’s growth
FV = PV * (1+r)n
12,500 = 8,000 * (1+r)8
1.5625 = (1 + r )8
1 + r = (1.5625)1/8
Solving for r = 5.74%
Based on the above analysis, the interest rate reduces with time for a fixed present value of a cash flow.
References
Day, A. L. (2012). Mastering cash flow and valuation modelling . Harlow: Pearson.
Helfert, E. A. (2003). Techniques of financial analysis: A guide to value creation . Boston: McGraw-Hill/Irwin.
Schroeder, R. G., Clark, M. W., & Cathey, J. M. (2001). Accounting: Theory and Analysis . John Wiley & Sons.
Shim, J. K. (2012). Time value of money and fair value accounting: Concepts and tools . Kent: Global Professional Publishing Ltd.
