Case 038Lending and leverageHard

A client buys a Rs 3 crore flat with an 80% loan at 9%, rent yielding 2.8% and prices rising 5% a year. What is his equity IRR over seven years, against buying with cash?

The situation

Mohit Arora-Bali plans to buy a Rs 3 crore flat to let out. He would borrow 80%, Rs 2.4 crore, at 9% over 20 years, an EMI of about Rs 215,934 a month. Stamp duty and registration add an illustrative 7% of the price, paid in cash. Rent is 2.8% of the flat's value a year, net of maintenance, and rises with the price. Prices rise 5% a year, and he sells after seven years, paying 1% in selling costs.

He could instead buy the same flat outright with cash. Ignore income tax, including any deduction for interest, and confirm current rules before relying on the figures.

Your task

Work out Mohit's equity IRR over seven years with the loan and with cash. Say when the loan helps and when it hurts.

Quick check

Does the 80% loan raise or lower Mohit's return here?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

With the loan, Mohit's seven-year equity IRR is about 2.6%; in cash it is about 6.5%. The flat earns about 7.8% a year, 2.8% rent plus 5% growth, less the costs of buying and selling, and the loan costs 9%, so every borrowed rupee loses money. Leverage only lifts the return once price growth passes about 7.4% a year. The loan also costs him about Rs 17.5 lakh a year from his own pocket in the first year.

Step 1What decides whether the loan helps?

A shopkeeper who borrows at 9% to stock goods that sell at a 7% margin loses on every extra unit, and loses faster the more he borrows. Leverage helps only while the asset earns more than the loan costs; below that line, it magnifies the shortfall instead of the gain. The flat earns 2.8% in rent plus 5% in price growth, about 7.8% a year, before the one-off costs of buying and selling. The loan costs 9%. On these numbers the loan is working against Mohit from the first month.

Step 2How do the cash flows run?

With the loan, Mohit puts in Rs 0.81 crore at the start: Rs 60 lakh of deposit and Rs 21 lakh of stamp duty. Each year the EMI of about Rs 25.9 lakh exceeds the rent, Rs 8.4 lakh in year 1, so he feeds in about Rs 17.5 lakh of his own money, a gap that narrows only slowly as rent rises. At year 7 the flat sells for Rs 4.22 crore less 1% costs, and Rs 1.98 crore of loan is still outstanding, because a 20-year loan repays little principal in its first seven years.

YearLevered: cash flowCash buyer: cash flow
0-81.0-321.0
1-17.58.4
2-17.18.8
3-16.79.3
4-16.29.7
5-15.710.2
6-15.210.7
7205.1429.2
IRR2.6%6.5%
Rs lakh, negative is money put in. The levered buyer puts in Rs 0.81 crore plus a yearly shortfall and receives Rs 2.05 crore net in year 7; the cash buyer puts in Rs 3.21 crore, collects rent and receives the full sale proceeds.
What each buyer has put in against what each owns, Rs crore80% loan at 9%123401234567owns 2.24put in 1.94All cash123401234567owns 4.22put in 2.53cash put in, net of rent receivedequity owned: flat value less loan outstanding
The levered buyer puts in Rs 1.94 crore over seven years, net of rent, and owns Rs 2.24 crore of equity at the end, while the cash buyer puts in Rs 3.21 crore up front and owns a flat worth Rs 4.22 crore.
Step 3At what growth rate does the loan start to help?

Run the IRR for price growth from 0% to 12% a year. The two lines cross near 7.4% growth; above it the loan lifts the return, below it the loan cuts it, and the levered line is far steeper on both sides. At 8% growth the levered IRR is 10.4% against 9.5% in cash; at 0% growth the levered buyer loses heavily while the cash buyer still earns roughly the rent less costs. That steepness is the real cost of leverage: it widens the range of outcomes Mohit has to live with.

Leverage steepens the line; it only helps to the right of the cross-20%-10%+10%+20%+30%0%0%3%5%8%12%Yearly rise in the flat's pricecross near 7.4% growthcase: levered 2.6%cash 6.5%80% loanall cash
The seven-year IRR rises far more steeply with price growth for the 80% loan than for the cash purchase; the lines cross near 7.4% growth, so at the case's 5% the loan lowers the return to 2.6% from 6.5%.

Close with the judgement and its limits. On these assumptions, the loan makes this flat a worse investment, not a better one, and only a view that prices will rise faster than about 7% a year would justify it. Tax can move the answer: interest deductions on a let-out property reduce the loan's cost, and the gain on sale is taxed; confirm current rules and rerun. Liquidity matters too: about Rs 18 lakh a year of negative carry has to come from his income every year.

Where candidates lose it

The common error is multiplying the price gain by five because the loan is 80%: 5% growth on 20% equity sounds like 25% a year. That ignores the 9% interest on the other 80% and the stamp duty, and it gets the sign of the effect wrong.

The second is leaving out the monthly shortfall. The EMI is far above the rent, and a candidate who counts only the deposit as Mohit's money overstates the levered return badly.

What the interviewer asks next

  • The loan rate falls to 7.5%. Where does the cross move?
  • How does a 3-year holding period change both IRRs, given the 7% stamp duty?
  • Mohit plans to live in the flat instead of letting it. How would you frame the comparison then?

Company names and figures are illustrative.