Weighted Average Cost of Commitment

As mentioned in a previous post, the weighted average cost of commitment, or WACC, is the rate we use to value the expected future payoffs of a relationship. Looking at it another way, it’s the rate of return we would expect from a relationship given what we have to invest. The rate is referred to as a “weighted average” because there are two components: the cost of equity and the cost of borrowing.

Cost of Equity (Re)
The cost of equity is the return you expect from your investment in the relationship – love, companionship, stability, bragging rights, conjugal rights, status elevation – whatever it is you envision the ideal relationship to be. The cost of equity also reflects the risk of whether or not and to what extent these benefits are ever realized. A higher risk means a higher cost of equity, and subsequently a lower present value.

The cost of equity can also be broken down into multiple components. The first component is the risk-free rate (Rf). The risk-free rate should be the rate of return you get from the safest investment possible. For most people, it’s a mother’s unconditional love. Anything above and beyond that is the return you expect for taking on additional risk.

This additional premium is calculated by subtracting the risk-free rate from the expected return on the market (Rm), which is simply the average return you get from all the relationships in your life. The difference is then multiplied by the person’s bipolar coefficient (β), which represents their emotional stability relative to most people. A person with a high beta will be really happy during the good times, but really miserable during the bad times.

The formula for computing the cost of equity is known as the Companionship Applicant Pricing Model (CAPM). Putting everything together, it looks like this:

Re = Rf + β(Rm – Rf)

In some cases you may need to add an additional asset-specific risk premium to account for risks not always captured in the CAPM formula, such as their age, maturity level, fat potential, etc.

Cost of Borrowing (Rd)
The second component of the WACC is the cost of borrowing. You’re not the only one with skin in the game; in-laws, relatives, and friends also have a stake in the relationship. When your companion receives unsolicited advice or turns to these sources for support, the relationship could be severely affected. So you have to factor in the cost of external sources of capital and what kind of strain they will put on the relationship.

Weighted Average
After you’ve computed both the cost of equity and the cost of borrowing, all you have to do is determine to what extent each component plays into the overall cost. If you think you’ll have to spend half your time together with the other person’s family, then you might want to give the cost of borrowing a 50% weighting. But if you live in a different state than the in-laws, you may only give it a 10% weighting. You then use this weighted average discount rate to determine the net present value of investing in the relationship.

Discount Rates and Present Value
Some may not be familiar with the concepts of discounting future benefits to compute a present value, so a brief explanation is in order (focus on the concepts rather than the math). Suppose someone promises to give you $110 a year from now if you give them $105 today. Based on past experience with this person, you know that there is a chance that he won’t deliver the full $110 as he promises. So you decide that if you’re going to take the risk, you want a 10% return per year. So what is the present value of his promise to pay you $110 in a year? The answer: $100. Accordingly, given your required rate of return (or discount rate), you should not give him the $105 he is asking for. If you were to use this same 10% discount rate for a promise of $110 in two years, you would only be willing to give him about $91 today.

Finance: An Approach to Relationships

Alright, I've decided on a theme for this blog. As a finance major, I have a very particular lens through which I see the world. And since we happen to be in the middle of a worldwide financial crisis, I thought it might be appropriate to explain finance principles and concepts by relating them to experiences we all share. Accordingly, my posts on this blog will focus on relationships, as well as life in general, from a financial perspective. I hope readers will find it entertaining and perhaps educational. (I've created a different blog for more general stuff: Chippy.com)To start off, I'll use one of the most common methodologies for valuing an investment - the income approach.

The income approach seeks to measure the future benefits that can be quantified in monetary terms. The process generally involves forecasting the future cash flows expected from an asset, and then discounting those cash flows to the present value using a discount rate that considers the inherent risks of obtaining those cash flows. So we will liken a relationship with another person to an asset or investment.

Before we enter into a relationship, we have to consider the "cash flows," a.k.a. benefits we might receive. How hot is the other person? Are they a good kisser? Can they cook? Will they make a lot of money? Would their family members make good in-laws? But wait; what we really want is net benefits, so we have to factor in their weaknesses. Are they a shopoholic? Do they have bad gas? These things decrease the value of our investment, so we can't forget them. Once we have the best possible knowledge we can obtain, we then project the net inflow of future benefits.

Now of course, predicting the future always involves some degree of uncertainty. We account for this by discounting the future benefits back to the present using our discount rate, which we'll call the WACC (weighted average cost of commitment). This rate considers the inherent risks of our decision. What if they get fat? What if they lose their job? What if their mom goes psycho and decides to hate you? All these things must be weighed in the calculation of our WACC, which should essentially represent the opportunity cost of our next best alternative.

Using the WACC to discount our future benefits will give us the net present value (NPV) of our relationship. If you want to get a more accurate calculation, you should factor in the tax benefits of children. Now in theory, you should only make the investment if the NPV is positive, but the higher the NPV the better. You can also compare your initial investment (engagement ring, time spent, etc.) with the flow of future benefits to calculate your internal rate of return (IRR). This rate should be higher than your WACC for the investment to make sense.

Now of course, a relationship decision should not be entirely based on the benefits you receive from the other person. In reality, you should invest in a relationship because you love the person simply for who they are, and perhaps who they can become. But let's be honest, the other stuff matters. The income approach can provide valuable insight for all relationships.