Question

Consider the following timeline detailing a stream of cash flows Date 0 2 3 4 ? $5000 $6000 $7000 $8000 Cash flow If the current market rate of interest is 8%, then the present value (PV) of this stream of cash flows is closest to

Answer 1

The present value (PV) of a stream of cash flows can be calculated by discounting each cash flow back to the present using the appropriate discount rate. In this case, the present value of the stream of cash flows is $21,467.62.

Step-by-step explanation:

The present value (PV) of a stream of cash flows can be calculated by discounting each cash flow back to the present using the appropriate discount rate. In this case, the stream of cash flows is $5000, $6000, $7000, and $8000, occurring at times 2, 3, 4, and ?. To calculate the present value, we need to find the present value factor for each cash flow based on the market rate of interest, which is 8%. The present value factor can be calculated using the formula:

Present Value Factor = 1 / (1 + i)^n

where i is the interest rate and n is the time period. Let's calculate the present value factors for each cash flow:

1. Present Value Factor for $5000 at time 2: 1 / (1 + 0.08)^2 = 0.8573
2. Present Value Factor for $6000 at time 3: 1 / (1 + 0.08)^3 = 0.7938
3. Present Value Factor for $7000 at time 4: 1 / (1 + 0.08)^4 = 0.7350
4. Present Value Factor for $8000 at time ?: 1 / (1 + 0.08)^? = x

To find the present value (PV) of the stream of cash flows, we multiply each cash flow by its respective present value factor and sum them up:

PV = $5000 * 0.8573 + $6000 * 0.7938 + $7000 * 0.7350 + $8000 * x

We don't have enough information about the time period for the cash flow of $8000, so we can't calculate its present value. However, if we assume that it occurs at time 5, we can calculate its present value factor:

Present Value Factor for $8000 at time 5: 1 / (1 + 0.08)^5 = 0.6806

Now, we can substitute this value into the present value formula:

PV = $5000 * 0.8573 + $6000 * 0.7938 + $7000 * 0.7350 + $8000 * 0.6806 = $21,467.62

Therefore, the closest present value (PV) of this stream of cash flows is $21,467.62.

Answer 2

The present value of a stream of cash flows is calculated by discounting each cash flow back to the present using the present value formula. For a bond example paying annual interest and principal at the end of its term, discounting at the market rate gives the current worth of the bond. Changing interest rates affect the present value of the future cash flows.

Step-by-step explanation:

The question involves calculating the present value (PV) of a stream of cash flows given a certain market rate of interest. To find the PV for each cash flow, we use the present value formula: PV = Cash Flow / (1 + i)^n, where 'i' is the interest rate and 'n' is the number of periods until the cash flow is received. In the context of the bond example given, the bond pays $240 in interest at the end of the first and second years, and $3,000 in principle at the end of the second year. The present value of this bond at an 8% discount rate can be found by discounting each payment back to the present.

If the discount rate is 8%, the first year's interest would be discounted as follows: PV = 240 / (1 + 0.08)^1. The second year's payments would need to account for both the interest and the principal: PV = (240 + 3000) / (1 + 0.08)^2. If the interest rates rise to 11%, the calculation would be similar but using 0.11 as the discount rate. These calculations would give us the present value of the bond at different discount rates, illustrating how the value of future cash flows changes with varying interest rates.