Cost of borrowing

Hello!

I’m stuck on the two questions related to the cost of borrowing and will be grateful for any advice.

Q1. Which loan is cheaper?

Given two loans with exactly the same amortization profile. Say the first option is domestic currency loan at 9% p.a. and the second one is 4% p.a. in USD.

The most obvious approach is to compare the rates in a single currency using the cross currency interest rate swap.

Clearly the differential between domestic and USD rates is priced in the swap rate and justified by many risk factors. But even if the swapped loans are equivalent, at the end of the day the reported financing expenses in domestic currency will be higher.

Q2. Is it meaningful to use the Present Value of the two loans (discounted at the relevant Sovereign rate) to decide which one is cheaper.

The interest rates have dropped recently and the company considers refinancing of existing Old loan with the New one of longer maturity. Both loans have bullet amortization schedule and the same interest rate.

Old 5 year @ 10%
New 10 year @ 10%

Over the 5 years the total interest amount paid for the New loan is twice as much higher:

Old 5 year 5 x 10% x 1bn = 500mm
New 10 year 10 x 10% x 1bn = 1bn

PV of Old 5Y loan discounted @ 5Y Govt rate 5% = 277mm
PV of New 10Y loan discounted @ 10Y Govt rate 7.5% = 259mm

259mm the refinancing with the new 10Y loan is preferred option regardless the greater total amount of interest expense.