# Project Appraisal: Money-Weighted Rate of Return, Time-Weighted Rate of Return and Linked Rate of Return

**What do we mean by appraisal?**

On a lighter note, appraisal is an act of assessing something or someone. Generally, we come across this word with regards to employees’ performance appraisal at workplace.

**What can be the main motive behind such appraisals?**

The answer is simple- Appraisals demonstrate the need for improvement.

Similarly, **assessing the viability or feasibility of a proposed project by the
lending institutions is called** **project
appraisal**. This is done to know the effect of each project for the company.
This means that **project appraisal is
done to know, how much the company has invested on the project and in** **return how much it is gaining from it.** It
is a tool that company’s use for choosing the best project that would help them
to attain their goal.

This leads us to the introduction of various measures of returns used for project appraisal-

- Money Weighted Rate of Return (MWRR)
- Time Weighted Rate of Return (TWRR)
- Linked Internal Rate of Return (LIRR).

**Money Weighted Rate of Return**

MWRR is a method to calculate the rate of return of a portfolio. It takes into consideration the impact of contributions to (inflow of cashflows), or withdrawals from (outflow of cashflow) the portfolio. It is mainly used to compute individual portfolio returns as timing and amount of contributions and withdrawals can be different for each individual investors’ portfolio.

A money-weighted rate of return is the discount rate at which the

Net present value =0,

or The present value of inflows= present value of outflows.

Money Weighted Rate of Return incorporates the size and timings of cashflows.

Outflows:

- The cost of investment purchased
- Reinvested dividends or interest
- Withdrawals

Inflows:

- The proceeds from any investment sold
- Dividends or interest received
- Contribution

Each inflow or outflow must be discounted back to the present using a rate (r) that will make **PV (inflows) = PV (outflows).**

For example, take a case where we buy one share of a stock for Rs.50 that pays an annual Rs.2 dividend, and sell it after two years for Rs.65. Our money-weighted rate of return will be a rate that satisfies the following equation:

Let’s have a look at the associated cashflows:

PV Inflows = Rs.2/ (1 + r) + Rs.2/ [(1 + r) ^2] + Rs.65/ [(1 + r) ^2].

PV Outflows = Rs.50.**Using PV Inflows = PV Outflows**

Solving for r using

**Time Weighted Rate of Return**

TWRR measures a funds’ compounded rate of growth over a specific time period. While TWRR measures the return of a funds’ investments, it does not consider the effect of investor cash moving in and out of a fund. Thus, TWRR is suitable for measuring the performance of marketable investment managers because they do not control when investor cash enters or exits their funds.

To get a better understanding of TWRR let’s have a look at the associated cashflows:

Investor A invests $1 million into Mutual Fund A on December 31. On August 15 of the following year, his portfolio is valued at $1,162,484. At that point (August 15), he adds $100,000 to Mutual Fund A, bringing the total value to $1,262,484.

By the end of the year, the portfolio has decreased in value to $1,192,328. The holding-period return for the first period, from December 31 to August 15, would be calculated as:

**Return = ($1,162,484 – $1,000,000) / $1,000,000 = 16.25%**

The holding-period return for the second period, from August 15 to December 31, would be calculated as:

**Return = ($1,192,328 – ($1,162,484 + $100,000)) / ($1,162,484 + $100,000) = -5.56%**

The second sub-period is created following the $100,000 deposit so that the rate of return is calculated reflecting that deposit with its new starting balance of $1,262,484 or ($1,162,484 + $100,000).

The time-weighted return for the two time periods is calculated by multiplying each sub period’s rate of return by each other. The first period is the period leading up to the deposit, and the second period is after the $100,000 deposit.

**Time-weighted return = [(1 + 16.25%) x (1 + (-5.56%))] – 1 = 9.79%**

But the point is that both the methods have disadvantages: TWRR requires fund values at all cashflow dates. MWRR may not have a unique solution and fund manager performance cannot be judged. If the fund performance is reasonably stable in the period of assessment, the TWRR and MWRR may give similar results. Then there comes Linked Internal Rate of Return (LIRR).

**Linked Internal Rate of Return **

The main drawback of TWRR is that it requires constant account valuations every time an external cash flow occurs. Money-weighted returns are simpler in that the portfolio only needs to be valued at the beginning and end of the period. The linked internal rate of return (LIRR) was developed to combine TWRR’s immunity to cash flows with MWRR’s ease of calculation.

LIRR attempts to approximate time-weighted returns by chain-linking money-weighted returns over reasonable time intervals. For example, if we calculate the money-weighted return every week in our month evaluation period, we could then just combine them for our month time-weighted return. This turns out to be a very accurate approximation of time-weighted returns, without valuing the portfolio at every cash flow.

Suppose the tenure of a fund is 3 years. We calculate return after every 1 year.

**So the equation is – (1+r1)(1+r2)(1+r3)= [(1+i)^3] **

where r1 represents ^{nd} year, r3 after 3^{rd} year and “i” represents the LIRR. The rate of return over each different sub-period is weighted according to the duration of the sub-period.

Therefore, it can be said that performance measurement is a vital part of overall performance evaluation as it answers the question of how much money we made in a period. I would like to conclude my article by the words spoken by a famous personality named Peter Drucker and I quote-“If you can’t measure it, you can’t manage it!” and that’s what project appraisal is all about.