Tile chips and dishwashers quit, but space is forever.

Bigger houses sell for more money.

In the hopeful algebra of remodeling, homeowners try to balance an equation with two sets of factors: what they want and how much they can afford, and what the job will cost and what they expect to get back on resale.

The formula isn't too challenging when a house that's in good shape is about to go on the market. Almost everybody knows that money spent on paint and touch-ups is part of the selling expense.

But the medium- to long-term payback of remodeling is murkier. The added value of a remodeling job fades as the materials and appliances wear out. Meanwhile, the value of the house is likely to rise anyway along with the market.

No amount of squinting will reveal a precise vanishing point, but there are strategies for figuring out the biggest bang tomorrow for a buck spent today.

When Angela and Jeff Sprau bought their 1928 Tudor house in Whitefish Bay, Wis., in 1995 for $204,000, they knew they were in for some remodeling.

The house was barely big enough for the couple and their baby. And though they hoped to stay in the house for years, they knew that a corporate relocation might be in the cards.

Over the next 11 years, they tried to calibrate their remodeling decisions to mirror the rapidly escalating expectations of Whitefish Bay home buyers and fit the changing needs of their growing family.

"I follow the local real estate market, and I knew that adding a master suite and updating the kitchen, especially in a vintage house, would be a big selling point," Angela Sprau said.

Remodeling magazine releases a survey every November that calculates the payback of common remodeling projects upon resale, assuming the house is sold within a year of the completion of the project.

Sal Alfano, editorial director for the magazine, said that the one thing that comes through loud and clear, year after year, is that adding functional space nearly always brings the biggest return.

That assumes that the square footage is "well designed," Alfano said. "There are a lot of ugly additions out there. If you're in a brick house and you just add a room with vinyl siding onto the side, that won't work. It should be tied to the facade and roof massing and be in scale."

Concocting a design from a list of ideas ripped from decorating magazines won't result in a coherent plan, and a confused house is hard to sell, said Thomas Weiher, president of Carmel Builders in Menomonee Falls, Wis.

"You need a design that fits with the current style of the property, to enhance it and expand on it, rather than bringing in something that's a clash. That probably devalues these projects more than anything, not having a complement to what it is that you started with," Weiher said.

There is a limit.

Alfano said the Remodeling magazine survey assumes that the house starts at the size of the typical American house, about 2,300 square feet. Adding a few hundred square feet to a house that size moves it up to the next-biggest category.

"But adding 500 square feet to an 8,000-square-foot house, well, that probably won't pay," he said.

Expanding a house so that it's significantly bigger than most houses in the neighborhood undermines payback, too.

The sweet spot is adding enough space so the house is more livable and not so much that it's out of whack with the immediate market.

Not all added space has the same payback.

Finishing a basement is one project that homeowners often expect will pay back in spades, but doesn't, Alfano said.

A simple playroom is viewed as only rudimentary space, but getting fancy gets iffy quickly.

The Spraus' first priority was adding a master suite to their three-bedroom, 11/2-bath home.

In 1999, for $70,000, they built onto a second-floor porch, adding a large bedroom with a vaulted ceiling, three closets and a full bath.

Bathrooms bring the biggest value to home buyers, according to a national analysis of the characteristics and prices of houses sold in 2004 conducted by G. Stacy Sirmans, a real estate professor at Florida State University in Tallahassee.

"If you're going to build something on, build a bathroom. It has the greatest effect," he said.

Other amenities, such as fireplaces, are important to fewer buyers, but those who care, care a lot. Adding a garage, which is really an improvement to the property, not the house, has an even greater impact on buyers.

People don't usually add bathrooms just to keep up with the neighbors. They add them because they'll use them, Alfano said. Everybody wants plenty of bathrooms, so the resale appeal is strong.

Bathrooms usually hold their value because porcelain fixtures, quality plumbing and decent-quality tile last for years, Alfano said.

When people add a master bath, they often want fancier finishes or fixtures -- like the multiple shower heads now in vogue -- and figure that future buyers will envision themselves enjoying a little pampering.

"When it comes to kitchens and baths, people have a tendency to get what they want," Weiher said. "With a guest bath or powder room, they want function. They'll keep it simple."

Kitchens are more complicated.

Unlike bathrooms, their functionality pivots on appliances as well as fixtures, and appliances wear out. Kitchen surfaces take much more of a beating than bathroom counters and floors.

Buyers might not know a dovetailed inside cabinet drawer joint when they see one, but they quickly size up the quality and condition of a kitchen that a seller claims is updated.

The shrinking value of a well-remodeled kitchen is "more a matter of style and wear than of actual age. If you put in all new stuff and your kids are little monsters, and you have a large number of animals, then in two years, it might not be updated anymore," said Diana Manning, coauthor of "Everything and the Kitchen Sink: Remodel Your Kitchen Without Losing Your Mind."

"Be honest with yourself about your lifestyle," she said. "It's not a crime to be messy, but if you are, admit it. If you get stainless, get brushed or get low-maintenance surfaces," to preserve the value of the renovation.

Remodelers say it's best to invest in high-quality cabinets, which last for decades, and medium-quality floors and counters. The floors and counters will wear out faster than top-quality goods, but they're easier and cheaper to upgrade later.

"If you put cheap stuff in an upscale house, it won't match the neighborhood and people will come in the kitchen and say, 'Why aren't the cabinets solid wood?' " Manning said. "But if you have a starter house and you want to improve it and sell it for a profit, and you put in granite counters and hand-painted tile, you'll price it out of the market. You've made it beautiful but you've probably raised it to where the neighborhood can't support that price because people who can afford that price don't want your neighborhood."

Sometimes homeowners try to justify prestige-brand appliances or fancy finishes by telling themselves that buyers will swoon at the quality, but that's not so, said Thomas R. Ortell, who heads the real estate associate degree program at the Milwaukee Area Technical College and owns Real Estate Renovation, a Butler, Wis., firm that buys, renovates and sells residential property.

"Buyers don't necessarily quantify the difference" between medium- and high-quality finishes and appliances, he said.

They want reassurance that the appliances work and that there's life left in the flooring and plumbing fixtures. But unless they are looking for a specific finish or appliance brand, they aren't going to pay more for a Sub-Zero refrigerator when an Amana keeps the root beer just as cool.

"You have to have two payback numbers: the functional payback, which includes adding square footage, upgrading mechanicals like plumbing and electrical, and improving the traffic flow. Above that, you're paying for what makes you feel good," Ortell said.