Skysearch Ltd $($SL$)$ has provided ARI with lease financing for a big optical telescope that

can take pictures of Earth$-$like environments around other planets and traces of life in their

atmospheres. SL has built this telescope at a cost of $$1,500,000.$ This unique telescope on

the market has a useful life of $15$ years and a modest residual value of $$400,000$ given the

rapid changes in this type of technology. The telescope$$s selling price would have been

$$2,000,000$ if it had been sold rather than leased to ARI.

$$Sylvain Durocher, $2024$

The following clauses are included in the arrangement signed by the two companies:

$$ Lease term of $15$ years $($from $1$ January $20$X$1)$;

$$ Annual rental payments of $$190,000$ from January $1,20$X$1$;

$$ Option to purchase the telescope for $$105,337$ at the end of the lease term;

$$ No restriction in the use of the telescope during the lease term.

ARI has expensed the first lease payment in its financial statements for the year ended $31$

December $20$X$1.$ No asset or liability have been recognized for this telescope. At $31$

December $20$X$1,$ ARI reports total assets of $$50,000,000$ and total liabilities of

$$38,000,000.$ ARI$$s creditors include the Royal Bank. ARI has signed a debt contract with

the bank that includes a convenant requiring ARI to maintain a maximum debt$-$to$-$equity

ratio $($Total liabilities $-$: Total equity$)$ of $3\mathrm{.}25.$

Required

$1)$ Compute the implicit rate of the contract. You can use a financial calculator or the

Excel software. Provide the details of your computation.