Topic №11: Evaluation of financial and economic efficiency of investment projects

Modified Net Present Value of MNPV
In the case when the barrier rate and reinvestment rate differ significantly, it makes sense (in terms of accuracy) to calculate NPV according to the following formula (taking into account that the funds received as a result of the investment are reinvested at a different rate):
MNPV - modified net present value,
CFt - cash inflow in the period t = 1, 2, ... n;
It - cash outflow in the period t = 0, 1, 2, ... n (in absolute value);
r- the barrier rate (discount rate);
d - level of reinvestments (interest rate based on possible income from reinvestment of received positive cash flows or rate of return on reinvestments);
n - the number of periods.
Example No. 1. Calculation of MNPV.
Investments - $ 115,000.
Income from investments in the first year: $ 32,000;
in the second year: $ 41,000;
in the third year: $ 43,750;
in the fourth year: $ 38,250.
The reinvestment rate is 6.6%.
The barrier rate is 9.2%.
For the 1st period: CF1 * (1 + d)^3 = 32000 * (1 + 0,066)3 = 38763,38$;
For the 2nd period: CF2 * (1 + d)^2 = 41000 * (1 + 0,066)2 = 46590,60$;
For the 3rd period: CF3 * (1 + d)^1 = 43750 * (1 + 0,066) = 46637,5$;
For the 4th period: CF4 * 1 = 38250 * 1 = 38250$.
Amount of compounded positive cash flows are equal: 38763,38 + 46590,60 + 46637,5 + 38250 = 170241,48$.
MNPV = 170241,48 / (1 + 0,092)^4 - 115000 = 119722,24 - 115000 = 4722,24$.
Answer: modified net present value is 4722,24$.
The formula for the indicator is modified net present value (MNPV), taking into account the variable barrier rate and the variable level of reinvestment:
MNPV - modified net present value,
CFt - cash inflow in the period t = 1, 2, ... n;
It - cash outflow in the period t = 0, 1, 2, ... n;
ri - the barrier rate (discount rate);
di - reinvestment rate;
n - the number of periods.
Example No. 2. MNPV at variable barrier rate.
Investments - $ 12800.
Income from investments in the first year: $ 7360;
in the second year: $ 5185;
in the third year: $ 6,270.
The reinvestment rate is 7.125% in the second year;
5.334% in the third year.
The barrier rate is 11.4% in the first year;
10.7% in the second year;
9.5% in the third year.
Determine the value of the modified net present value for the investment project.
Composition (1+ rt) = (1 + 0,114) * (1 + 0,107) * (1 + 0,095) = 1,3503518
For the 1st period: CF1 * (1 + 0,07125) * (1 + 0,05334) = 7360 * 1,07125 * 1,05334 = $8304,95;
For the 2nd period : CF2 * (1 + 0,05334) = 5185 * 1,05334 = $5461,57;
For the 3rd period : CF3 * 1 = $6270;
MNPV = (8304,95 + 5461,57 + 6270) / 1,3503518 - 12800 = $2038,001
Answer. Modified net present value (MNPV) is $ 2038.
MNPV makes possible to most accurately know the net profit from an investment project in absolute terms (dollars, soums), because not only barrier rates, but also reinvestment rates are taken into account.
The modified internal rate of return MIRR
The procedure for calculating the modified internal rate of return MIRR:
1. Calculate the total discounted value of all cash outflows and all cash inflows.
Discounting is carried out at the price of the project financing source (Capital Cost, CC or WACC), i.e. at the barrier rate. The increase is carried out at an interest rate equal to the level of reinvestment.
The accrued value of the inflows is called Net Terminal Value (NTV).
2. Establish a discount factor that takes into account the total present value of the outflows and inflows. The discount rate that balances the true value of the investment (PV) with its terminal value is called MIRR.